KILLED
proof of input_YFNioLH2dw.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# AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished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), 49 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), 34 ms]
    (14) typed CpxTrs
    (15) RewriteLemmaProof [LOWER BOUND(ID), 615 ms]
    (16) typed CpxTrs
    (17) RewriteLemmaProof [LOWER BOUND(ID), 6705 ms]
    (18) typed CpxTrs
    (19) RewriteLemmaProof [LOWER BOUND(ID), 1827 ms]
    (20) BEST
        (21) proven lower bound
            (22) LowerBoundPropagationProof [FINISHED, 0 ms]
            (23) BOUNDS(n^1, INF)
        (24) typed CpxTrs
(25) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms]
(26) CpxWeightedTrs
    (27) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
    (28) CpxTypedWeightedTrs
    (29) CompletionProof [UPPER BOUND(ID), 0 ms]
    (30) CpxTypedWeightedCompleteTrs
        (31) NarrowingProof [BOTH BOUNDS(ID, ID), 55 ms]
        (32) CpxTypedWeightedCompleteTrs
        (33) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 9 ms]
        (34) CpxRNTS
        (35) InliningProof [UPPER BOUND(ID), 414 ms]
        (36) CpxRNTS
        (37) SimplificationProof [BOTH BOUNDS(ID, ID), 8 ms]
        (38) CpxRNTS
    (39) CompletionProof [UPPER BOUND(ID), 0 ms]
    (40) CpxTypedWeightedCompleteTrs
        (41) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 3 ms]
        (42) CpxRNTS
(43) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms]
(44) CdtProblem
    (45) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
    (46) CdtProblem
    (47) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
    (48) CdtProblem
    (49) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
    (50) CpxRelTRS
        (51) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
        (52) CpxTRS
        (53) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
        (54) CpxWeightedTrs
            (55) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
            (56) CpxTypedWeightedTrs
            (57) CompletionProof [UPPER BOUND(ID), 0 ms]
            (58) CpxTypedWeightedCompleteTrs
                (59) NarrowingProof [BOTH BOUNDS(ID, ID), 774 ms]
                (60) CpxTypedWeightedCompleteTrs
                (61) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
                (62) CpxRNTS
                (63) InliningProof [UPPER BOUND(ID), 830 ms]
                (64) CpxRNTS
                (65) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
                (66) CpxRNTS
            (67) CompletionProof [UPPER BOUND(ID), 0 ms]
            (68) CpxTypedWeightedCompleteTrs
                (69) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
                (70) CpxRNTS
    (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
    (72) CdtProblem
        (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (74) CdtProblem
        (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (76) CdtProblem
        (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (78) CdtProblem
        (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (80) CdtProblem
        (81) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (82) CdtProblem
        (83) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (84) CdtProblem
        (85) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (86) CdtProblem
        (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (88) CdtProblem
        (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (90) CdtProblem
        (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (92) CdtProblem
        (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (94) CdtProblem
        (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (96) CdtProblem
        (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (98) CdtProblem
        (99) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (100) CdtProblem
        (101) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (102) CdtProblem
        (103) CdtGraphSplitRhsProof [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), 0 ms]
        (118) CdtProblem
        (119) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (120) CdtProblem
        (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (122) CdtProblem
        (123) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (124) CdtProblem
        (125) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (126) CdtProblem
        (127) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (128) CdtProblem
        (129) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (130) CdtProblem
        (131) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 3 ms]
        (132) CdtProblem
        (133) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (134) CdtProblem
        (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (136) CdtProblem
        (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (138) CdtProblem
        (139) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (140) CdtProblem
        (141) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (142) CdtProblem
        (143) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (144) CdtProblem
        (145) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 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), 52 ms]
        (154) CdtProblem
        (155) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (156) CdtProblem
        (157) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (158) CdtProblem
        (159) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (160) CdtProblem
        (161) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 18 ms]
        (162) CdtProblem
        (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 1 ms]
        (164) CdtProblem
        (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 4 ms]
        (166) CdtProblem
        (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (168) CdtProblem
        (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 54 ms]
        (170) CdtProblem
        (171) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (172) CdtProblem
        (173) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms]
        (174) CdtProblem
        (175) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (176) CdtProblem
        (177) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (178) CdtProblem
        (179) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (180) CdtProblem
        (181) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms]
        (182) CdtProblem
        (183) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (184) CdtProblem
        (185) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 39 ms]
        (186) CdtProblem
        (187) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (188) CdtProblem
        (189) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 30 ms]
        (190) CdtProblem
        (191) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (192) CdtProblem
        (193) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 ms]
        (194) CdtProblem
        (195) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (196) CdtProblem
        (197) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 14 ms]
        (198) CdtProblem
        (199) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 11 ms]
        (200) CdtProblem
        (201) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 16 ms]
        (202) CdtProblem
        (203) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (204) CdtProblem
        (205) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (206) CdtProblem
        (207) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (208) CdtProblem
        (209) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms]
        (210) CdtProblem
        (211) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 13 ms]
        (212) CdtProblem
        (213) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (214) CdtProblem
        (215) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 13 ms]
        (216) CdtProblem
        (217) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 51 ms]
        (218) CdtProblem
        (219) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (220) CdtProblem
        (221) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 38 ms]
        (222) CdtProblem
        (223) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms]
        (224) CdtProblem
        (225) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (226) CdtProblem
        (227) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (228) CdtProblem
        (229) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 25 ms]
        (230) CdtProblem
        (231) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (232) CdtProblem
        (233) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 36 ms]
        (234) CdtProblem
        (235) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (236) CdtProblem
        (237) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
        (238) CdtProblem
        (239) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms]
        (240) CdtProblem
        (241) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 32 ms]
        (242) CdtProblem
        (243) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms]
        (244) CdtProblem
        (245) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 30 ms]
        (246) CdtProblem
        (247) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (248) CdtProblem
        (249) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 35 ms]
        (250) CdtProblem
        (251) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 9 ms]
        (252) CdtProblem
        (253) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms]
        (254) CdtProblem
        (255) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 42 ms]
        (256) CdtProblem
        (257) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms]
        (258) CdtProblem
        (259) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 13 ms]
        (260) 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__U11(tt, V2) -> a__U12(a__isNat(V2))
   a__U12(tt) -> tt
   a__U21(tt) -> tt
   a__U31(tt, N) -> mark(N)
   a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N)
   a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M)))
   a__isNat(0) -> tt
   a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2)
   a__isNat(s(V1)) -> a__U21(a__isNat(V1))
   a__plus(N, 0) -> a__U31(a__isNat(N), N)
   a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N)
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
   mark(U12(X)) -> a__U12(mark(X))
   mark(isNat(X)) -> a__isNat(X)
   mark(U21(X)) -> a__U21(mark(X))
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
   mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
   mark(tt) -> tt
   mark(s(X)) -> s(mark(X))
   mark(0) -> 0
   a__U11(X1, X2) -> U11(X1, X2)
   a__U12(X) -> U12(X)
   a__isNat(X) -> isNat(X)
   a__U21(X) -> U21(X)
   a__U31(X1, X2) -> U31(X1, X2)
   a__U41(X1, X2, X3) -> U41(X1, X2, X3)
   a__U42(X1, X2, X3) -> U42(X1, X2, X3)
   a__plus(X1, X2) -> plus(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__U11(tt, V2) -> a__U12(a__isNat(V2))
   a__U12(tt) -> tt
   a__U21(tt) -> tt
   a__U31(tt, N) -> mark(N)
   a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N)
   a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M)))
   a__isNat(0') -> tt
   a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2)
   a__isNat(s(V1)) -> a__U21(a__isNat(V1))
   a__plus(N, 0') -> a__U31(a__isNat(N), N)
   a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N)
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
   mark(U12(X)) -> a__U12(mark(X))
   mark(isNat(X)) -> a__isNat(X)
   mark(U21(X)) -> a__U21(mark(X))
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
   mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
   mark(tt) -> tt
   mark(s(X)) -> s(mark(X))
   mark(0') -> 0'
   a__U11(X1, X2) -> U11(X1, X2)
   a__U12(X) -> U12(X)
   a__isNat(X) -> isNat(X)
   a__U21(X) -> U21(X)
   a__U31(X1, X2) -> U31(X1, X2)
   a__U41(X1, X2, X3) -> U41(X1, X2, X3)
   a__U42(X1, X2, X3) -> U42(X1, X2, X3)
   a__plus(X1, X2) -> plus(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__U11(tt, V2) -> a__U12(a__isNat(V2))
   a__U12(tt) -> tt
   a__U21(tt) -> tt
   a__U31(tt, N) -> mark(N)
   a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N)
   a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M)))
   a__isNat(0) -> tt
   a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2)
   a__isNat(s(V1)) -> a__U21(a__isNat(V1))
   a__plus(N, 0) -> a__U31(a__isNat(N), N)
   a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N)
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2)
   mark(U12(X)) -> a__U12(mark(X))
   mark(isNat(X)) -> a__isNat(X)
   mark(U21(X)) -> a__U21(mark(X))
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2)
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3)
   mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3)
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2))
   mark(tt) -> tt
   mark(s(X)) -> s(mark(X))
   mark(0) -> 0
   a__U11(X1, X2) -> U11(X1, X2)
   a__U12(X) -> U12(X)
   a__isNat(X) -> isNat(X)
   a__U21(X) -> U21(X)
   a__U31(X1, X2) -> U31(X1, X2)
   a__U41(X1, X2, X3) -> U41(X1, X2, X3)
   a__U42(X1, X2, X3) -> U42(X1, X2, X3)
   a__plus(X1, X2) -> plus(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__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0))
   A__U11(z0, z1) -> c1
   A__U12(tt) -> c2
   A__U12(z0) -> c3
   A__U21(tt) -> c4
   A__U21(z0) -> c5
   A__U31(tt, z0) -> c6(MARK(z0))
   A__U31(z0, z1) -> c7
   A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1))
   A__U41(z0, z1, z2) -> c9
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U42(z0, z1, z2) -> c12
   A__ISNAT(0) -> c13
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__U21(a__isNat(z0)), A__ISNAT(z0))
   A__ISNAT(z0) -> c16
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   A__PLUS(z0, z1) -> c19
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(U12(z0)) -> c21(A__U12(mark(z0)), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U21(z0)) -> c23(A__U21(mark(z0)), MARK(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(tt) -> c29
   MARK(s(z0)) -> c30(MARK(z0))
   MARK(0) -> c31
S tuples:
   A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0))
   A__U11(z0, z1) -> c1
   A__U12(tt) -> c2
   A__U12(z0) -> c3
   A__U21(tt) -> c4
   A__U21(z0) -> c5
   A__U31(tt, z0) -> c6(MARK(z0))
   A__U31(z0, z1) -> c7
   A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1))
   A__U41(z0, z1, z2) -> c9
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U42(z0, z1, z2) -> c12
   A__ISNAT(0) -> c13
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__U21(a__isNat(z0)), A__ISNAT(z0))
   A__ISNAT(z0) -> c16
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   A__PLUS(z0, z1) -> c19
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(U12(z0)) -> c21(A__U12(mark(z0)), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U21(z0)) -> c23(A__U21(mark(z0)), MARK(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(tt) -> c29
   MARK(s(z0)) -> c30(MARK(z0))
   MARK(0) -> c31
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U11_2, A__U12_1, A__U21_1, A__U31_2, A__U41_3, A__U42_3, A__ISNAT_1, A__PLUS_2, MARK_1

Compound Symbols:   c_2, c1, c2, c3, c4, c5, c6_1, c7, c8_2, c9, c10_2, c11_2, c12, c13, c14_2, c15_2, c16, c17_2, c18_2, c19, c20_2, c21_2, c22_1, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29, c30_1, c31


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

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

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


The TRS R consists of the following rules:

   A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0))
   A__U11(z0, z1) -> c1
   A__U12(tt) -> c2
   A__U12(z0) -> c3
   A__U21(tt) -> c4
   A__U21(z0) -> c5
   A__U31(tt, z0) -> c6(MARK(z0))
   A__U31(z0, z1) -> c7
   A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1))
   A__U41(z0, z1, z2) -> c9
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U42(z0, z1, z2) -> c12
   A__ISNAT(0) -> c13
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__U21(a__isNat(z0)), A__ISNAT(z0))
   A__ISNAT(z0) -> c16
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   A__PLUS(z0, z1) -> c19
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(U12(z0)) -> c21(A__U12(mark(z0)), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U21(z0)) -> c23(A__U21(mark(z0)), MARK(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(tt) -> c29
   MARK(s(z0)) -> c30(MARK(z0))
   MARK(0) -> c31

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

   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0

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

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

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


The TRS R consists of the following rules:

   A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0))
   A__U11(z0, z1) -> c1
   A__U12(tt) -> c2
   A__U12(z0) -> c3
   A__U21(tt) -> c4
   A__U21(z0) -> c5
   A__U31(tt, z0) -> c6(MARK(z0))
   A__U31(z0, z1) -> c7
   A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1))
   A__U41(z0, z1, z2) -> c9
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U42(z0, z1, z2) -> c12
   A__ISNAT(0') -> c13
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__U21(a__isNat(z0)), A__ISNAT(z0))
   A__ISNAT(z0) -> c16
   A__PLUS(z0, 0') -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   A__PLUS(z0, z1) -> c19
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(U12(z0)) -> c21(A__U12(mark(z0)), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U21(z0)) -> c23(A__U21(mark(z0)), MARK(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(tt) -> c29
   MARK(s(z0)) -> c30(MARK(z0))
   MARK(0') -> c31

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

   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0') -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0') -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0') -> 0'

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

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

(12)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0))
A__U11(z0, z1) -> c1
A__U12(tt) -> c2
A__U12(z0) -> c3
A__U21(tt) -> c4
A__U21(z0) -> c5
A__U31(tt, z0) -> c6(MARK(z0))
A__U31(z0, z1) -> c7
A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1))
A__U41(z0, z1, z2) -> c9
A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U42(z0, z1, z2) -> c12
A__ISNAT(0') -> c13
A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
A__ISNAT(s(z0)) -> c15(A__U21(a__isNat(z0)), A__ISNAT(z0))
A__ISNAT(z0) -> c16
A__PLUS(z0, 0') -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
A__PLUS(z0, z1) -> c19
MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
MARK(U12(z0)) -> c21(A__U12(mark(z0)), MARK(z0))
MARK(isNat(z0)) -> c22(A__ISNAT(z0))
MARK(U21(z0)) -> c23(A__U21(mark(z0)), MARK(z0))
MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c29
MARK(s(z0)) -> c30(MARK(z0))
MARK(0') -> c31
a__U11(tt, z0) -> a__U12(a__isNat(z0))
a__U11(z0, z1) -> U11(z0, z1)
a__U12(tt) -> tt
a__U12(z0) -> U12(z0)
a__U21(tt) -> tt
a__U21(z0) -> U21(z0)
a__U31(tt, z0) -> mark(z0)
a__U31(z0, z1) -> U31(z0, z1)
a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
a__U41(z0, z1, z2) -> U41(z0, z1, z2)
a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U42(z0, z1, z2) -> U42(z0, z1, z2)
a__isNat(0') -> tt
a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
a__isNat(s(z0)) -> a__U21(a__isNat(z0))
a__isNat(z0) -> isNat(z0)
a__plus(z0, 0') -> a__U31(a__isNat(z0), z0)
a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
mark(U12(z0)) -> a__U12(mark(z0))
mark(isNat(z0)) -> a__isNat(z0)
mark(U21(z0)) -> a__U21(mark(z0))
mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c:c1
tt :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c :: c2:c3 -> c13:c14:c15:c16 -> c:c1
A__U12 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c2:c3
a__isNat :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
A__ISNAT :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c13:c14:c15:c16
c1 :: c:c1
c2 :: c2:c3
c3 :: c2:c3
A__U21 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c4:c5
c4 :: c4:c5
c5 :: c4:c5
A__U31 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c6:c7
c6 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c6:c7
MARK :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c7 :: c6:c7
A__U41 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c8:c9
c8 :: c10:c11:c12 -> c13:c14:c15:c16 -> c8:c9
A__U42 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c10:c11:c12
c9 :: c8:c9
c10 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c10:c11:c12
A__PLUS :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c17:c18:c19
mark :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c11 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c10:c11:c12
c12 :: c10:c11:c12
0' :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c13 :: c13:c14:c15:c16
plus :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c14 :: c:c1 -> c13:c14:c15:c16 -> c13:c14:c15:c16
s :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c15 :: c4:c5 -> c13:c14:c15:c16 -> c13:c14:c15:c16
c16 :: c13:c14:c15:c16
c17 :: c6:c7 -> c13:c14:c15:c16 -> c17:c18:c19
c18 :: c8:c9 -> c13:c14:c15:c16 -> c17:c18:c19
c19 :: c17:c18:c19
U11 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c20 :: c:c1 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U12 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c21 :: c2:c3 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
isNat :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c22 :: c13:c14:c15:c16 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U21 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c23 :: c4:c5 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U31 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c24 :: c6:c7 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U41 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c25 :: c8:c9 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U42 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c26 :: c10:c11:c12 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c27 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c28 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c29 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c30 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c31 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
a__U11 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U12 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U21 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U31 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U41 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U42 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__plus :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
hole_c:c11_32 :: c:c1
hole_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U422_32 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
hole_c2:c33_32 :: c2:c3
hole_c13:c14:c15:c164_32 :: c13:c14:c15:c16
hole_c4:c55_32 :: c4:c5
hole_c6:c76_32 :: c6:c7
hole_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c317_32 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
hole_c8:c98_32 :: c8:c9
hole_c10:c11:c129_32 :: c10:c11:c12
hole_c17:c18:c1910_32 :: c17:c18:c19
gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32 :: Nat -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
gen_c13:c14:c15:c1612_32 :: Nat -> c13:c14:c15:c16
gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32 :: Nat -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31

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

(13) OrderProof (LOWER BOUND(ID))
Heuristically decided to analyse the following defined symbols:
A__U11, a__isNat, A__ISNAT, A__U31, MARK, A__U41, A__U42, A__PLUS, mark, a__U11, a__U31, a__U41, a__U42, a__plus

They will be analysed ascendingly in the following order:
a__isNat < A__U11
A__U11 = A__ISNAT
A__U11 < MARK
a__isNat < A__ISNAT
a__isNat < A__U41
a__isNat < A__PLUS
a__isNat < mark
a__isNat = a__U11
a__isNat < a__U41
a__isNat < a__plus
A__ISNAT < MARK
A__ISNAT < A__U41
A__ISNAT < A__PLUS
A__U31 = MARK
A__U31 = A__U41
A__U31 = A__U42
A__U31 = A__PLUS
MARK = A__U41
MARK = A__U42
MARK = A__PLUS
mark < MARK
A__U41 = A__U42
A__U41 = A__PLUS
A__U42 = A__PLUS
mark < A__U42
a__U11 < mark
mark = a__U31
mark = a__U41
mark = a__U42
mark = a__plus
a__U31 = a__U41
a__U31 = a__U42
a__U31 = a__plus
a__U41 = a__U42
a__U41 = a__plus
a__U42 = a__plus

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

(14)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0))
A__U11(z0, z1) -> c1
A__U12(tt) -> c2
A__U12(z0) -> c3
A__U21(tt) -> c4
A__U21(z0) -> c5
A__U31(tt, z0) -> c6(MARK(z0))
A__U31(z0, z1) -> c7
A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1))
A__U41(z0, z1, z2) -> c9
A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U42(z0, z1, z2) -> c12
A__ISNAT(0') -> c13
A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
A__ISNAT(s(z0)) -> c15(A__U21(a__isNat(z0)), A__ISNAT(z0))
A__ISNAT(z0) -> c16
A__PLUS(z0, 0') -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
A__PLUS(z0, z1) -> c19
MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
MARK(U12(z0)) -> c21(A__U12(mark(z0)), MARK(z0))
MARK(isNat(z0)) -> c22(A__ISNAT(z0))
MARK(U21(z0)) -> c23(A__U21(mark(z0)), MARK(z0))
MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c29
MARK(s(z0)) -> c30(MARK(z0))
MARK(0') -> c31
a__U11(tt, z0) -> a__U12(a__isNat(z0))
a__U11(z0, z1) -> U11(z0, z1)
a__U12(tt) -> tt
a__U12(z0) -> U12(z0)
a__U21(tt) -> tt
a__U21(z0) -> U21(z0)
a__U31(tt, z0) -> mark(z0)
a__U31(z0, z1) -> U31(z0, z1)
a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
a__U41(z0, z1, z2) -> U41(z0, z1, z2)
a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U42(z0, z1, z2) -> U42(z0, z1, z2)
a__isNat(0') -> tt
a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
a__isNat(s(z0)) -> a__U21(a__isNat(z0))
a__isNat(z0) -> isNat(z0)
a__plus(z0, 0') -> a__U31(a__isNat(z0), z0)
a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
mark(U12(z0)) -> a__U12(mark(z0))
mark(isNat(z0)) -> a__isNat(z0)
mark(U21(z0)) -> a__U21(mark(z0))
mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c:c1
tt :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c :: c2:c3 -> c13:c14:c15:c16 -> c:c1
A__U12 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c2:c3
a__isNat :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
A__ISNAT :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c13:c14:c15:c16
c1 :: c:c1
c2 :: c2:c3
c3 :: c2:c3
A__U21 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c4:c5
c4 :: c4:c5
c5 :: c4:c5
A__U31 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c6:c7
c6 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c6:c7
MARK :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c7 :: c6:c7
A__U41 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c8:c9
c8 :: c10:c11:c12 -> c13:c14:c15:c16 -> c8:c9
A__U42 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c10:c11:c12
c9 :: c8:c9
c10 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c10:c11:c12
A__PLUS :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c17:c18:c19
mark :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c11 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c10:c11:c12
c12 :: c10:c11:c12
0' :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c13 :: c13:c14:c15:c16
plus :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c14 :: c:c1 -> c13:c14:c15:c16 -> c13:c14:c15:c16
s :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c15 :: c4:c5 -> c13:c14:c15:c16 -> c13:c14:c15:c16
c16 :: c13:c14:c15:c16
c17 :: c6:c7 -> c13:c14:c15:c16 -> c17:c18:c19
c18 :: c8:c9 -> c13:c14:c15:c16 -> c17:c18:c19
c19 :: c17:c18:c19
U11 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c20 :: c:c1 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U12 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c21 :: c2:c3 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
isNat :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c22 :: c13:c14:c15:c16 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U21 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c23 :: c4:c5 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U31 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c24 :: c6:c7 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U41 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c25 :: c8:c9 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U42 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c26 :: c10:c11:c12 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c27 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c28 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c29 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c30 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c31 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
a__U11 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U12 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U21 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U31 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U41 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U42 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__plus :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
hole_c:c11_32 :: c:c1
hole_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U422_32 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
hole_c2:c33_32 :: c2:c3
hole_c13:c14:c15:c164_32 :: c13:c14:c15:c16
hole_c4:c55_32 :: c4:c5
hole_c6:c76_32 :: c6:c7
hole_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c317_32 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
hole_c8:c98_32 :: c8:c9
hole_c10:c11:c129_32 :: c10:c11:c12
hole_c17:c18:c1910_32 :: c17:c18:c19
gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32 :: Nat -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
gen_c13:c14:c15:c1612_32 :: Nat -> c13:c14:c15:c16
gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32 :: Nat -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31


Generator Equations:
gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(0) <=> tt
gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(x, 1)) <=> plus(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(x), tt)
gen_c13:c14:c15:c1612_32(0) <=> c13
gen_c13:c14:c15:c1612_32(+(x, 1)) <=> c14(c(c2, c13), gen_c13:c14:c15:c1612_32(x))
gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32(0) <=> c22(c13)
gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32(+(x, 1)) <=> c20(c(c2, c13), gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32(x))


The following defined symbols remain to be analysed:
a__U11, A__U11, a__isNat, A__ISNAT, A__U31, MARK, A__U41, A__U42, A__PLUS, mark, a__U31, a__U41, a__U42, a__plus

They will be analysed ascendingly in the following order:
a__isNat < A__U11
A__U11 = A__ISNAT
A__U11 < MARK
a__isNat < A__ISNAT
a__isNat < A__U41
a__isNat < A__PLUS
a__isNat < mark
a__isNat = a__U11
a__isNat < a__U41
a__isNat < a__plus
A__ISNAT < MARK
A__ISNAT < A__U41
A__ISNAT < A__PLUS
A__U31 = MARK
A__U31 = A__U41
A__U31 = A__U42
A__U31 = A__PLUS
MARK = A__U41
MARK = A__U42
MARK = A__PLUS
mark < MARK
A__U41 = A__U42
A__U41 = A__PLUS
A__U42 = A__PLUS
mark < A__U42
a__U11 < mark
mark = a__U31
mark = a__U41
mark = a__U42
mark = a__plus
a__U31 = a__U41
a__U31 = a__U42
a__U31 = a__plus
a__U41 = a__U42
a__U41 = a__plus
a__U42 = a__plus

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

(15) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
a__isNat(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(1, n963_32))) -> *14_32, rt in Omega(0)

Induction Base:
a__isNat(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(1, 0)))

Induction Step:
a__isNat(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(1, +(n963_32, 1)))) ->_R^Omega(0)
a__U11(a__isNat(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(1, n963_32))), tt) ->_IH
a__U11(*14_32, tt)

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__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0))
A__U11(z0, z1) -> c1
A__U12(tt) -> c2
A__U12(z0) -> c3
A__U21(tt) -> c4
A__U21(z0) -> c5
A__U31(tt, z0) -> c6(MARK(z0))
A__U31(z0, z1) -> c7
A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1))
A__U41(z0, z1, z2) -> c9
A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U42(z0, z1, z2) -> c12
A__ISNAT(0') -> c13
A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
A__ISNAT(s(z0)) -> c15(A__U21(a__isNat(z0)), A__ISNAT(z0))
A__ISNAT(z0) -> c16
A__PLUS(z0, 0') -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
A__PLUS(z0, z1) -> c19
MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
MARK(U12(z0)) -> c21(A__U12(mark(z0)), MARK(z0))
MARK(isNat(z0)) -> c22(A__ISNAT(z0))
MARK(U21(z0)) -> c23(A__U21(mark(z0)), MARK(z0))
MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c29
MARK(s(z0)) -> c30(MARK(z0))
MARK(0') -> c31
a__U11(tt, z0) -> a__U12(a__isNat(z0))
a__U11(z0, z1) -> U11(z0, z1)
a__U12(tt) -> tt
a__U12(z0) -> U12(z0)
a__U21(tt) -> tt
a__U21(z0) -> U21(z0)
a__U31(tt, z0) -> mark(z0)
a__U31(z0, z1) -> U31(z0, z1)
a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
a__U41(z0, z1, z2) -> U41(z0, z1, z2)
a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U42(z0, z1, z2) -> U42(z0, z1, z2)
a__isNat(0') -> tt
a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
a__isNat(s(z0)) -> a__U21(a__isNat(z0))
a__isNat(z0) -> isNat(z0)
a__plus(z0, 0') -> a__U31(a__isNat(z0), z0)
a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
mark(U12(z0)) -> a__U12(mark(z0))
mark(isNat(z0)) -> a__isNat(z0)
mark(U21(z0)) -> a__U21(mark(z0))
mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c:c1
tt :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c :: c2:c3 -> c13:c14:c15:c16 -> c:c1
A__U12 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c2:c3
a__isNat :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
A__ISNAT :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c13:c14:c15:c16
c1 :: c:c1
c2 :: c2:c3
c3 :: c2:c3
A__U21 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c4:c5
c4 :: c4:c5
c5 :: c4:c5
A__U31 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c6:c7
c6 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c6:c7
MARK :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c7 :: c6:c7
A__U41 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c8:c9
c8 :: c10:c11:c12 -> c13:c14:c15:c16 -> c8:c9
A__U42 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c10:c11:c12
c9 :: c8:c9
c10 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c10:c11:c12
A__PLUS :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c17:c18:c19
mark :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c11 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c10:c11:c12
c12 :: c10:c11:c12
0' :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c13 :: c13:c14:c15:c16
plus :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c14 :: c:c1 -> c13:c14:c15:c16 -> c13:c14:c15:c16
s :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c15 :: c4:c5 -> c13:c14:c15:c16 -> c13:c14:c15:c16
c16 :: c13:c14:c15:c16
c17 :: c6:c7 -> c13:c14:c15:c16 -> c17:c18:c19
c18 :: c8:c9 -> c13:c14:c15:c16 -> c17:c18:c19
c19 :: c17:c18:c19
U11 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c20 :: c:c1 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U12 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c21 :: c2:c3 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
isNat :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c22 :: c13:c14:c15:c16 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U21 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c23 :: c4:c5 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U31 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c24 :: c6:c7 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U41 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c25 :: c8:c9 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U42 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c26 :: c10:c11:c12 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c27 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c28 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c29 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c30 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c31 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
a__U11 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U12 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U21 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U31 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U41 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U42 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__plus :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
hole_c:c11_32 :: c:c1
hole_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U422_32 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
hole_c2:c33_32 :: c2:c3
hole_c13:c14:c15:c164_32 :: c13:c14:c15:c16
hole_c4:c55_32 :: c4:c5
hole_c6:c76_32 :: c6:c7
hole_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c317_32 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
hole_c8:c98_32 :: c8:c9
hole_c10:c11:c129_32 :: c10:c11:c12
hole_c17:c18:c1910_32 :: c17:c18:c19
gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32 :: Nat -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
gen_c13:c14:c15:c1612_32 :: Nat -> c13:c14:c15:c16
gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32 :: Nat -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31


Lemmas:
a__isNat(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(1, n963_32))) -> *14_32, rt in Omega(0)


Generator Equations:
gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(0) <=> tt
gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(x, 1)) <=> plus(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(x), tt)
gen_c13:c14:c15:c1612_32(0) <=> c13
gen_c13:c14:c15:c1612_32(+(x, 1)) <=> c14(c(c2, c13), gen_c13:c14:c15:c1612_32(x))
gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32(0) <=> c22(c13)
gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32(+(x, 1)) <=> c20(c(c2, c13), gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32(x))


The following defined symbols remain to be analysed:
a__U11, A__U11, A__ISNAT, A__U31, MARK, A__U41, A__U42, A__PLUS, mark, a__U31, a__U41, a__U42, a__plus

They will be analysed ascendingly in the following order:
a__isNat < A__U11
A__U11 = A__ISNAT
A__U11 < MARK
a__isNat < A__ISNAT
a__isNat < A__U41
a__isNat < A__PLUS
a__isNat < mark
a__isNat = a__U11
a__isNat < a__U41
a__isNat < a__plus
A__ISNAT < MARK
A__ISNAT < A__U41
A__ISNAT < A__PLUS
A__U31 = MARK
A__U31 = A__U41
A__U31 = A__U42
A__U31 = A__PLUS
MARK = A__U41
MARK = A__U42
MARK = A__PLUS
mark < MARK
A__U41 = A__U42
A__U41 = A__PLUS
A__U42 = A__PLUS
mark < A__U42
a__U11 < mark
mark = a__U31
mark = a__U41
mark = a__U42
mark = a__plus
a__U31 = a__U41
a__U31 = a__U42
a__U31 = a__plus
a__U41 = a__U42
a__U41 = a__plus
a__U42 = a__plus

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

(17) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
mark(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(n558289_32)) -> gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(n558289_32), rt in Omega(0)

Induction Base:
mark(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(0)) ->_R^Omega(0)
tt

Induction Step:
mark(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(n558289_32, 1))) ->_R^Omega(0)
a__plus(mark(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(n558289_32)), mark(tt)) ->_IH
a__plus(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(c558290_32), mark(tt)) ->_R^Omega(0)
a__plus(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(n558289_32), tt) ->_R^Omega(0)
plus(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(n558289_32), tt)

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__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0))
A__U11(z0, z1) -> c1
A__U12(tt) -> c2
A__U12(z0) -> c3
A__U21(tt) -> c4
A__U21(z0) -> c5
A__U31(tt, z0) -> c6(MARK(z0))
A__U31(z0, z1) -> c7
A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1))
A__U41(z0, z1, z2) -> c9
A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U42(z0, z1, z2) -> c12
A__ISNAT(0') -> c13
A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
A__ISNAT(s(z0)) -> c15(A__U21(a__isNat(z0)), A__ISNAT(z0))
A__ISNAT(z0) -> c16
A__PLUS(z0, 0') -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
A__PLUS(z0, z1) -> c19
MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
MARK(U12(z0)) -> c21(A__U12(mark(z0)), MARK(z0))
MARK(isNat(z0)) -> c22(A__ISNAT(z0))
MARK(U21(z0)) -> c23(A__U21(mark(z0)), MARK(z0))
MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c29
MARK(s(z0)) -> c30(MARK(z0))
MARK(0') -> c31
a__U11(tt, z0) -> a__U12(a__isNat(z0))
a__U11(z0, z1) -> U11(z0, z1)
a__U12(tt) -> tt
a__U12(z0) -> U12(z0)
a__U21(tt) -> tt
a__U21(z0) -> U21(z0)
a__U31(tt, z0) -> mark(z0)
a__U31(z0, z1) -> U31(z0, z1)
a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
a__U41(z0, z1, z2) -> U41(z0, z1, z2)
a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U42(z0, z1, z2) -> U42(z0, z1, z2)
a__isNat(0') -> tt
a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
a__isNat(s(z0)) -> a__U21(a__isNat(z0))
a__isNat(z0) -> isNat(z0)
a__plus(z0, 0') -> a__U31(a__isNat(z0), z0)
a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
mark(U12(z0)) -> a__U12(mark(z0))
mark(isNat(z0)) -> a__isNat(z0)
mark(U21(z0)) -> a__U21(mark(z0))
mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c:c1
tt :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c :: c2:c3 -> c13:c14:c15:c16 -> c:c1
A__U12 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c2:c3
a__isNat :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
A__ISNAT :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c13:c14:c15:c16
c1 :: c:c1
c2 :: c2:c3
c3 :: c2:c3
A__U21 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c4:c5
c4 :: c4:c5
c5 :: c4:c5
A__U31 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c6:c7
c6 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c6:c7
MARK :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c7 :: c6:c7
A__U41 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c8:c9
c8 :: c10:c11:c12 -> c13:c14:c15:c16 -> c8:c9
A__U42 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c10:c11:c12
c9 :: c8:c9
c10 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c10:c11:c12
A__PLUS :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c17:c18:c19
mark :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c11 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c10:c11:c12
c12 :: c10:c11:c12
0' :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c13 :: c13:c14:c15:c16
plus :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c14 :: c:c1 -> c13:c14:c15:c16 -> c13:c14:c15:c16
s :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c15 :: c4:c5 -> c13:c14:c15:c16 -> c13:c14:c15:c16
c16 :: c13:c14:c15:c16
c17 :: c6:c7 -> c13:c14:c15:c16 -> c17:c18:c19
c18 :: c8:c9 -> c13:c14:c15:c16 -> c17:c18:c19
c19 :: c17:c18:c19
U11 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c20 :: c:c1 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U12 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c21 :: c2:c3 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
isNat :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c22 :: c13:c14:c15:c16 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U21 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c23 :: c4:c5 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U31 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c24 :: c6:c7 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U41 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c25 :: c8:c9 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U42 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c26 :: c10:c11:c12 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c27 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c28 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c29 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c30 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c31 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
a__U11 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U12 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U21 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U31 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U41 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U42 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__plus :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
hole_c:c11_32 :: c:c1
hole_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U422_32 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
hole_c2:c33_32 :: c2:c3
hole_c13:c14:c15:c164_32 :: c13:c14:c15:c16
hole_c4:c55_32 :: c4:c5
hole_c6:c76_32 :: c6:c7
hole_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c317_32 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
hole_c8:c98_32 :: c8:c9
hole_c10:c11:c129_32 :: c10:c11:c12
hole_c17:c18:c1910_32 :: c17:c18:c19
gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32 :: Nat -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
gen_c13:c14:c15:c1612_32 :: Nat -> c13:c14:c15:c16
gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32 :: Nat -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31


Lemmas:
a__isNat(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(1, n963_32))) -> *14_32, rt in Omega(0)
mark(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(n558289_32)) -> gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(n558289_32), rt in Omega(0)


Generator Equations:
gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(0) <=> tt
gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(x, 1)) <=> plus(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(x), tt)
gen_c13:c14:c15:c1612_32(0) <=> c13
gen_c13:c14:c15:c1612_32(+(x, 1)) <=> c14(c(c2, c13), gen_c13:c14:c15:c1612_32(x))
gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32(0) <=> c22(c13)
gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32(+(x, 1)) <=> c20(c(c2, c13), gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32(x))


The following defined symbols remain to be analysed:
a__U41, A__U11, A__ISNAT, A__U31, MARK, A__U41, A__U42, A__PLUS, a__U31, a__U42, a__plus

They will be analysed ascendingly in the following order:
A__U11 = A__ISNAT
A__U11 < MARK
A__ISNAT < MARK
A__ISNAT < A__U41
A__ISNAT < A__PLUS
A__U31 = MARK
A__U31 = A__U41
A__U31 = A__U42
A__U31 = A__PLUS
MARK = A__U41
MARK = A__U42
MARK = A__PLUS
mark < MARK
A__U41 = A__U42
A__U41 = A__PLUS
A__U42 = A__PLUS
mark < A__U42
mark = a__U31
mark = a__U41
mark = a__U42
mark = a__plus
a__U31 = a__U41
a__U31 = a__U42
a__U31 = a__plus
a__U41 = a__U42
a__U41 = a__plus
a__U42 = a__plus

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

(19) RewriteLemmaProof (LOWER BOUND(ID))
Proved the following rewrite lemma:
MARK(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(1, n744339_32))) -> *14_32, rt in Omega(n744339_32)

Induction Base:
MARK(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(1, 0)))

Induction Step:
MARK(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(1, +(n744339_32, 1)))) ->_R^Omega(1)
c27(A__PLUS(mark(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(1, n744339_32))), mark(tt)), MARK(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(1, n744339_32)))) ->_L^Omega(0)
c27(A__PLUS(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(1, n744339_32)), mark(tt)), MARK(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(1, n744339_32)))) ->_L^Omega(0)
c27(A__PLUS(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(1, n744339_32)), gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(0)), MARK(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(1, n744339_32)))) ->_R^Omega(1)
c27(c19, MARK(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(1, n744339_32)))) ->_IH
c27(c19, *14_32)

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

(20)
Complex Obligation (BEST)

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

(21)
Obligation:
Proved the lower bound n^1 for the following obligation:

Innermost TRS:
Rules:
A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0))
A__U11(z0, z1) -> c1
A__U12(tt) -> c2
A__U12(z0) -> c3
A__U21(tt) -> c4
A__U21(z0) -> c5
A__U31(tt, z0) -> c6(MARK(z0))
A__U31(z0, z1) -> c7
A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1))
A__U41(z0, z1, z2) -> c9
A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U42(z0, z1, z2) -> c12
A__ISNAT(0') -> c13
A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
A__ISNAT(s(z0)) -> c15(A__U21(a__isNat(z0)), A__ISNAT(z0))
A__ISNAT(z0) -> c16
A__PLUS(z0, 0') -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
A__PLUS(z0, z1) -> c19
MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
MARK(U12(z0)) -> c21(A__U12(mark(z0)), MARK(z0))
MARK(isNat(z0)) -> c22(A__ISNAT(z0))
MARK(U21(z0)) -> c23(A__U21(mark(z0)), MARK(z0))
MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c29
MARK(s(z0)) -> c30(MARK(z0))
MARK(0') -> c31
a__U11(tt, z0) -> a__U12(a__isNat(z0))
a__U11(z0, z1) -> U11(z0, z1)
a__U12(tt) -> tt
a__U12(z0) -> U12(z0)
a__U21(tt) -> tt
a__U21(z0) -> U21(z0)
a__U31(tt, z0) -> mark(z0)
a__U31(z0, z1) -> U31(z0, z1)
a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
a__U41(z0, z1, z2) -> U41(z0, z1, z2)
a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U42(z0, z1, z2) -> U42(z0, z1, z2)
a__isNat(0') -> tt
a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
a__isNat(s(z0)) -> a__U21(a__isNat(z0))
a__isNat(z0) -> isNat(z0)
a__plus(z0, 0') -> a__U31(a__isNat(z0), z0)
a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
mark(U12(z0)) -> a__U12(mark(z0))
mark(isNat(z0)) -> a__isNat(z0)
mark(U21(z0)) -> a__U21(mark(z0))
mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c:c1
tt :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c :: c2:c3 -> c13:c14:c15:c16 -> c:c1
A__U12 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c2:c3
a__isNat :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
A__ISNAT :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c13:c14:c15:c16
c1 :: c:c1
c2 :: c2:c3
c3 :: c2:c3
A__U21 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c4:c5
c4 :: c4:c5
c5 :: c4:c5
A__U31 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c6:c7
c6 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c6:c7
MARK :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c7 :: c6:c7
A__U41 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c8:c9
c8 :: c10:c11:c12 -> c13:c14:c15:c16 -> c8:c9
A__U42 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c10:c11:c12
c9 :: c8:c9
c10 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c10:c11:c12
A__PLUS :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c17:c18:c19
mark :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c11 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c10:c11:c12
c12 :: c10:c11:c12
0' :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c13 :: c13:c14:c15:c16
plus :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c14 :: c:c1 -> c13:c14:c15:c16 -> c13:c14:c15:c16
s :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c15 :: c4:c5 -> c13:c14:c15:c16 -> c13:c14:c15:c16
c16 :: c13:c14:c15:c16
c17 :: c6:c7 -> c13:c14:c15:c16 -> c17:c18:c19
c18 :: c8:c9 -> c13:c14:c15:c16 -> c17:c18:c19
c19 :: c17:c18:c19
U11 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c20 :: c:c1 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U12 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c21 :: c2:c3 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
isNat :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c22 :: c13:c14:c15:c16 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U21 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c23 :: c4:c5 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U31 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c24 :: c6:c7 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U41 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c25 :: c8:c9 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U42 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c26 :: c10:c11:c12 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c27 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c28 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c29 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c30 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c31 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
a__U11 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U12 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U21 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U31 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U41 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U42 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__plus :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
hole_c:c11_32 :: c:c1
hole_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U422_32 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
hole_c2:c33_32 :: c2:c3
hole_c13:c14:c15:c164_32 :: c13:c14:c15:c16
hole_c4:c55_32 :: c4:c5
hole_c6:c76_32 :: c6:c7
hole_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c317_32 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
hole_c8:c98_32 :: c8:c9
hole_c10:c11:c129_32 :: c10:c11:c12
hole_c17:c18:c1910_32 :: c17:c18:c19
gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32 :: Nat -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
gen_c13:c14:c15:c1612_32 :: Nat -> c13:c14:c15:c16
gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32 :: Nat -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31


Lemmas:
a__isNat(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(1, n963_32))) -> *14_32, rt in Omega(0)
mark(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(n558289_32)) -> gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(n558289_32), rt in Omega(0)


Generator Equations:
gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(0) <=> tt
gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(x, 1)) <=> plus(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(x), tt)
gen_c13:c14:c15:c1612_32(0) <=> c13
gen_c13:c14:c15:c1612_32(+(x, 1)) <=> c14(c(c2, c13), gen_c13:c14:c15:c1612_32(x))
gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32(0) <=> c22(c13)
gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32(+(x, 1)) <=> c20(c(c2, c13), gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32(x))


The following defined symbols remain to be analysed:
MARK, A__U31, A__U41, A__U42, A__PLUS

They will be analysed ascendingly in the following order:
A__U31 = MARK
A__U31 = A__U41
A__U31 = A__U42
A__U31 = A__PLUS
MARK = A__U41
MARK = A__U42
MARK = A__PLUS
A__U41 = A__U42
A__U41 = A__PLUS
A__U42 = A__PLUS

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

(22) LowerBoundPropagationProof (FINISHED)
Propagated lower bound.
----------------------------------------

(23)
BOUNDS(n^1, INF)

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

(24)
Obligation:
Innermost TRS:
Rules:
A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0))
A__U11(z0, z1) -> c1
A__U12(tt) -> c2
A__U12(z0) -> c3
A__U21(tt) -> c4
A__U21(z0) -> c5
A__U31(tt, z0) -> c6(MARK(z0))
A__U31(z0, z1) -> c7
A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1))
A__U41(z0, z1, z2) -> c9
A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
A__U42(z0, z1, z2) -> c12
A__ISNAT(0') -> c13
A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
A__ISNAT(s(z0)) -> c15(A__U21(a__isNat(z0)), A__ISNAT(z0))
A__ISNAT(z0) -> c16
A__PLUS(z0, 0') -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
A__PLUS(z0, z1) -> c19
MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
MARK(U12(z0)) -> c21(A__U12(mark(z0)), MARK(z0))
MARK(isNat(z0)) -> c22(A__ISNAT(z0))
MARK(U21(z0)) -> c23(A__U21(mark(z0)), MARK(z0))
MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
MARK(tt) -> c29
MARK(s(z0)) -> c30(MARK(z0))
MARK(0') -> c31
a__U11(tt, z0) -> a__U12(a__isNat(z0))
a__U11(z0, z1) -> U11(z0, z1)
a__U12(tt) -> tt
a__U12(z0) -> U12(z0)
a__U21(tt) -> tt
a__U21(z0) -> U21(z0)
a__U31(tt, z0) -> mark(z0)
a__U31(z0, z1) -> U31(z0, z1)
a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
a__U41(z0, z1, z2) -> U41(z0, z1, z2)
a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
a__U42(z0, z1, z2) -> U42(z0, z1, z2)
a__isNat(0') -> tt
a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
a__isNat(s(z0)) -> a__U21(a__isNat(z0))
a__isNat(z0) -> isNat(z0)
a__plus(z0, 0') -> a__U31(a__isNat(z0), z0)
a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
a__plus(z0, z1) -> plus(z0, z1)
mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
mark(U12(z0)) -> a__U12(mark(z0))
mark(isNat(z0)) -> a__isNat(z0)
mark(U21(z0)) -> a__U21(mark(z0))
mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
mark(tt) -> tt
mark(s(z0)) -> s(mark(z0))
mark(0') -> 0'

Types:
A__U11 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c:c1
tt :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c :: c2:c3 -> c13:c14:c15:c16 -> c:c1
A__U12 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c2:c3
a__isNat :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
A__ISNAT :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c13:c14:c15:c16
c1 :: c:c1
c2 :: c2:c3
c3 :: c2:c3
A__U21 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c4:c5
c4 :: c4:c5
c5 :: c4:c5
A__U31 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c6:c7
c6 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c6:c7
MARK :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c7 :: c6:c7
A__U41 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c8:c9
c8 :: c10:c11:c12 -> c13:c14:c15:c16 -> c8:c9
A__U42 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c10:c11:c12
c9 :: c8:c9
c10 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c10:c11:c12
A__PLUS :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> c17:c18:c19
mark :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c11 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c10:c11:c12
c12 :: c10:c11:c12
0' :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c13 :: c13:c14:c15:c16
plus :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c14 :: c:c1 -> c13:c14:c15:c16 -> c13:c14:c15:c16
s :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c15 :: c4:c5 -> c13:c14:c15:c16 -> c13:c14:c15:c16
c16 :: c13:c14:c15:c16
c17 :: c6:c7 -> c13:c14:c15:c16 -> c17:c18:c19
c18 :: c8:c9 -> c13:c14:c15:c16 -> c17:c18:c19
c19 :: c17:c18:c19
U11 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c20 :: c:c1 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U12 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c21 :: c2:c3 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
isNat :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c22 :: c13:c14:c15:c16 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U21 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c23 :: c4:c5 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U31 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c24 :: c6:c7 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U41 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c25 :: c8:c9 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
U42 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
c26 :: c10:c11:c12 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c27 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c28 :: c17:c18:c19 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c29 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c30 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31 -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
c31 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
a__U11 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U12 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U21 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U31 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U41 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__U42 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
a__plus :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42 -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
hole_c:c11_32 :: c:c1
hole_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U422_32 :: tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
hole_c2:c33_32 :: c2:c3
hole_c13:c14:c15:c164_32 :: c13:c14:c15:c16
hole_c4:c55_32 :: c4:c5
hole_c6:c76_32 :: c6:c7
hole_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c317_32 :: c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31
hole_c8:c98_32 :: c8:c9
hole_c10:c11:c129_32 :: c10:c11:c12
hole_c17:c18:c1910_32 :: c17:c18:c19
gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32 :: Nat -> tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U42
gen_c13:c14:c15:c1612_32 :: Nat -> c13:c14:c15:c16
gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32 :: Nat -> c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c31


Lemmas:
a__isNat(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(1, n963_32))) -> *14_32, rt in Omega(0)
mark(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(n558289_32)) -> gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(n558289_32), rt in Omega(0)
MARK(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(1, n744339_32))) -> *14_32, rt in Omega(n744339_32)


Generator Equations:
gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(0) <=> tt
gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(+(x, 1)) <=> plus(gen_tt:0':plus:s:U11:U12:isNat:U21:U31:U41:U4211_32(x), tt)
gen_c13:c14:c15:c1612_32(0) <=> c13
gen_c13:c14:c15:c1612_32(+(x, 1)) <=> c14(c(c2, c13), gen_c13:c14:c15:c1612_32(x))
gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32(0) <=> c22(c13)
gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32(+(x, 1)) <=> c20(c(c2, c13), gen_c20:c21:c22:c23:c24:c25:c26:c27:c28:c29:c30:c3113_32(x))


The following defined symbols remain to be analysed:
A__U31, A__U41, A__U42, A__PLUS

They will be analysed ascendingly in the following order:
A__U31 = MARK
A__U31 = A__U41
A__U31 = A__U42
A__U31 = A__PLUS
MARK = A__U41
MARK = A__U42
MARK = A__PLUS
A__U41 = A__U42
A__U41 = A__PLUS
A__U42 = A__PLUS

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

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

(26)
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__U11(tt, V2) -> a__U12(a__isNat(V2)) [1]
   a__U12(tt) -> tt [1]
   a__U21(tt) -> tt [1]
   a__U31(tt, N) -> mark(N) [1]
   a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N) [1]
   a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__isNat(0) -> tt [1]
   a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) [1]
   a__isNat(s(V1)) -> a__U21(a__isNat(V1)) [1]
   a__plus(N, 0) -> a__U31(a__isNat(N), N) [1]
   a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N) [1]
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1]
   mark(U12(X)) -> a__U12(mark(X)) [1]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(U21(X)) -> a__U21(mark(X)) [1]
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1]
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1]
   mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) [1]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(tt) -> tt [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(0) -> 0 [1]
   a__U11(X1, X2) -> U11(X1, X2) [1]
   a__U12(X) -> U12(X) [1]
   a__isNat(X) -> isNat(X) [1]
   a__U21(X) -> U21(X) [1]
   a__U31(X1, X2) -> U31(X1, X2) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__U42(X1, X2, X3) -> U42(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]

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

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

(28)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   a__U11(tt, V2) -> a__U12(a__isNat(V2)) [1]
   a__U12(tt) -> tt [1]
   a__U21(tt) -> tt [1]
   a__U31(tt, N) -> mark(N) [1]
   a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N) [1]
   a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__isNat(0) -> tt [1]
   a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) [1]
   a__isNat(s(V1)) -> a__U21(a__isNat(V1)) [1]
   a__plus(N, 0) -> a__U31(a__isNat(N), N) [1]
   a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N) [1]
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1]
   mark(U12(X)) -> a__U12(mark(X)) [1]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(U21(X)) -> a__U21(mark(X)) [1]
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1]
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1]
   mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) [1]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(tt) -> tt [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(0) -> 0 [1]
   a__U11(X1, X2) -> U11(X1, X2) [1]
   a__U12(X) -> U12(X) [1]
   a__isNat(X) -> isNat(X) [1]
   a__U21(X) -> U21(X) [1]
   a__U31(X1, X2) -> U31(X1, X2) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__U42(X1, X2, X3) -> U42(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]

The TRS has the following type information:
a__U11 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
tt :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U12 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__isNat :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U21 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U31 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
mark :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U41 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U42 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
s :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__plus :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
0 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
plus :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U11 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U12 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
isNat :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U21 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U31 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U41 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U42 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42

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

(29) 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:

   a__isNat_1
   mark_1
   a__U21_1
   a__U42_3
   a__plus_2
   a__U41_3
   a__U31_2
   a__U11_2
   a__U12_1

Due to the following rules being added:
none

And the following fresh constants: none

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

(30)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   a__U11(tt, V2) -> a__U12(a__isNat(V2)) [1]
   a__U12(tt) -> tt [1]
   a__U21(tt) -> tt [1]
   a__U31(tt, N) -> mark(N) [1]
   a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N) [1]
   a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__isNat(0) -> tt [1]
   a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) [1]
   a__isNat(s(V1)) -> a__U21(a__isNat(V1)) [1]
   a__plus(N, 0) -> a__U31(a__isNat(N), N) [1]
   a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N) [1]
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1]
   mark(U12(X)) -> a__U12(mark(X)) [1]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(U21(X)) -> a__U21(mark(X)) [1]
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1]
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1]
   mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) [1]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(tt) -> tt [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(0) -> 0 [1]
   a__U11(X1, X2) -> U11(X1, X2) [1]
   a__U12(X) -> U12(X) [1]
   a__isNat(X) -> isNat(X) [1]
   a__U21(X) -> U21(X) [1]
   a__U31(X1, X2) -> U31(X1, X2) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__U42(X1, X2, X3) -> U42(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]

The TRS has the following type information:
a__U11 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
tt :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U12 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__isNat :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U21 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U31 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
mark :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U41 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U42 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
s :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__plus :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
0 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
plus :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U11 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U12 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
isNat :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U21 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U31 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U41 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U42 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42

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

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

(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__U11(tt, 0) -> a__U12(tt) [2]
   a__U11(tt, plus(V1', V2')) -> a__U12(a__U11(a__isNat(V1'), V2')) [2]
   a__U11(tt, s(V1'')) -> a__U12(a__U21(a__isNat(V1''))) [2]
   a__U11(tt, V2) -> a__U12(isNat(V2)) [2]
   a__U12(tt) -> tt [1]
   a__U21(tt) -> tt [1]
   a__U31(tt, N) -> mark(N) [1]
   a__U41(tt, M, 0) -> a__U42(tt, M, 0) [2]
   a__U41(tt, M, plus(V11, V2'')) -> a__U42(a__U11(a__isNat(V11), V2''), M, plus(V11, V2'')) [2]
   a__U41(tt, M, s(V12)) -> a__U42(a__U21(a__isNat(V12)), M, s(V12)) [2]
   a__U41(tt, M, N) -> a__U42(isNat(N), M, N) [2]
   a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__isNat(0) -> tt [1]
   a__isNat(plus(0, V2)) -> a__U11(tt, V2) [2]
   a__isNat(plus(plus(V13, V21), V2)) -> a__U11(a__U11(a__isNat(V13), V21), V2) [2]
   a__isNat(plus(s(V14), V2)) -> a__U11(a__U21(a__isNat(V14)), V2) [2]
   a__isNat(plus(V1, V2)) -> a__U11(isNat(V1), V2) [2]
   a__isNat(s(0)) -> a__U21(tt) [2]
   a__isNat(s(plus(V15, V22))) -> a__U21(a__U11(a__isNat(V15), V22)) [2]
   a__isNat(s(s(V16))) -> a__U21(a__U21(a__isNat(V16))) [2]
   a__isNat(s(V1)) -> a__U21(isNat(V1)) [2]
   a__plus(0, 0) -> a__U31(tt, 0) [2]
   a__plus(plus(V17, V23), 0) -> a__U31(a__U11(a__isNat(V17), V23), plus(V17, V23)) [2]
   a__plus(s(V18), 0) -> a__U31(a__U21(a__isNat(V18)), s(V18)) [2]
   a__plus(N, 0) -> a__U31(isNat(N), N) [2]
   a__plus(N, s(0)) -> a__U41(tt, 0, N) [2]
   a__plus(N, s(plus(V19, V24))) -> a__U41(a__U11(a__isNat(V19), V24), plus(V19, V24), N) [2]
   a__plus(N, s(s(V110))) -> a__U41(a__U21(a__isNat(V110)), s(V110), N) [2]
   a__plus(N, s(M)) -> a__U41(isNat(M), M, N) [2]
   mark(U11(U11(X159, X259), X2)) -> a__U11(a__U11(mark(X159), X259), X2) [2]
   mark(U11(U12(X73), X2)) -> a__U11(a__U12(mark(X73)), X2) [2]
   mark(U11(isNat(X74), X2)) -> a__U11(a__isNat(X74), X2) [2]
   mark(U11(U21(X75), X2)) -> a__U11(a__U21(mark(X75)), X2) [2]
   mark(U11(U31(X160, X260), X2)) -> a__U11(a__U31(mark(X160), X260), X2) [2]
   mark(U11(U41(X161, X261, X327), X2)) -> a__U11(a__U41(mark(X161), X261, X327), X2) [2]
   mark(U11(U42(X162, X262, X328), X2)) -> a__U11(a__U42(mark(X162), X262, X328), X2) [2]
   mark(U11(plus(X163, X263), X2)) -> a__U11(a__plus(mark(X163), mark(X263)), X2) [2]
   mark(U11(tt, X2)) -> a__U11(tt, X2) [2]
   mark(U11(s(X76), X2)) -> a__U11(s(mark(X76)), X2) [2]
   mark(U11(0, X2)) -> a__U11(0, X2) [2]
   mark(U12(U11(X164, X264))) -> a__U12(a__U11(mark(X164), X264)) [2]
   mark(U12(U12(X77))) -> a__U12(a__U12(mark(X77))) [2]
   mark(U12(isNat(X78))) -> a__U12(a__isNat(X78)) [2]
   mark(U12(U21(X79))) -> a__U12(a__U21(mark(X79))) [2]
   mark(U12(U31(X165, X265))) -> a__U12(a__U31(mark(X165), X265)) [2]
   mark(U12(U41(X166, X266, X329))) -> a__U12(a__U41(mark(X166), X266, X329)) [2]
   mark(U12(U42(X167, X267, X330))) -> a__U12(a__U42(mark(X167), X267, X330)) [2]
   mark(U12(plus(X168, X268))) -> a__U12(a__plus(mark(X168), mark(X268))) [2]
   mark(U12(tt)) -> a__U12(tt) [2]
   mark(U12(s(X80))) -> a__U12(s(mark(X80))) [2]
   mark(U12(0)) -> a__U12(0) [2]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(U21(U11(X169, X269))) -> a__U21(a__U11(mark(X169), X269)) [2]
   mark(U21(U12(X81))) -> a__U21(a__U12(mark(X81))) [2]
   mark(U21(isNat(X82))) -> a__U21(a__isNat(X82)) [2]
   mark(U21(U21(X83))) -> a__U21(a__U21(mark(X83))) [2]
   mark(U21(U31(X170, X270))) -> a__U21(a__U31(mark(X170), X270)) [2]
   mark(U21(U41(X171, X271, X331))) -> a__U21(a__U41(mark(X171), X271, X331)) [2]
   mark(U21(U42(X172, X272, X332))) -> a__U21(a__U42(mark(X172), X272, X332)) [2]
   mark(U21(plus(X173, X273))) -> a__U21(a__plus(mark(X173), mark(X273))) [2]
   mark(U21(tt)) -> a__U21(tt) [2]
   mark(U21(s(X84))) -> a__U21(s(mark(X84))) [2]
   mark(U21(0)) -> a__U21(0) [2]
   mark(U31(U11(X174, X274), X2)) -> a__U31(a__U11(mark(X174), X274), X2) [2]
   mark(U31(U12(X85), X2)) -> a__U31(a__U12(mark(X85)), X2) [2]
   mark(U31(isNat(X86), X2)) -> a__U31(a__isNat(X86), X2) [2]
   mark(U31(U21(X87), X2)) -> a__U31(a__U21(mark(X87)), X2) [2]
   mark(U31(U31(X175, X275), X2)) -> a__U31(a__U31(mark(X175), X275), X2) [2]
   mark(U31(U41(X176, X276, X333), X2)) -> a__U31(a__U41(mark(X176), X276, X333), X2) [2]
   mark(U31(U42(X177, X277, X334), X2)) -> a__U31(a__U42(mark(X177), X277, X334), X2) [2]
   mark(U31(plus(X178, X278), X2)) -> a__U31(a__plus(mark(X178), mark(X278)), X2) [2]
   mark(U31(tt, X2)) -> a__U31(tt, X2) [2]
   mark(U31(s(X88), X2)) -> a__U31(s(mark(X88)), X2) [2]
   mark(U31(0, X2)) -> a__U31(0, X2) [2]
   mark(U41(U11(X179, X279), X2, X3)) -> a__U41(a__U11(mark(X179), X279), X2, X3) [2]
   mark(U41(U12(X89), X2, X3)) -> a__U41(a__U12(mark(X89)), X2, X3) [2]
   mark(U41(isNat(X90), X2, X3)) -> a__U41(a__isNat(X90), X2, X3) [2]
   mark(U41(U21(X91), X2, X3)) -> a__U41(a__U21(mark(X91)), X2, X3) [2]
   mark(U41(U31(X180, X280), X2, X3)) -> a__U41(a__U31(mark(X180), X280), X2, X3) [2]
   mark(U41(U41(X181, X281, X335), X2, X3)) -> a__U41(a__U41(mark(X181), X281, X335), X2, X3) [2]
   mark(U41(U42(X182, X282, X336), X2, X3)) -> a__U41(a__U42(mark(X182), X282, X336), X2, X3) [2]
   mark(U41(plus(X183, X283), X2, X3)) -> a__U41(a__plus(mark(X183), mark(X283)), X2, X3) [2]
   mark(U41(tt, X2, X3)) -> a__U41(tt, X2, X3) [2]
   mark(U41(s(X92), X2, X3)) -> a__U41(s(mark(X92)), X2, X3) [2]
   mark(U41(0, X2, X3)) -> a__U41(0, X2, X3) [2]
   mark(U42(U11(X184, X284), X2, X3)) -> a__U42(a__U11(mark(X184), X284), X2, X3) [2]
   mark(U42(U12(X93), X2, X3)) -> a__U42(a__U12(mark(X93)), X2, X3) [2]
   mark(U42(isNat(X94), X2, X3)) -> a__U42(a__isNat(X94), X2, X3) [2]
   mark(U42(U21(X95), X2, X3)) -> a__U42(a__U21(mark(X95)), X2, X3) [2]
   mark(U42(U31(X185, X285), X2, X3)) -> a__U42(a__U31(mark(X185), X285), X2, X3) [2]
   mark(U42(U41(X186, X286, X337), X2, X3)) -> a__U42(a__U41(mark(X186), X286, X337), X2, X3) [2]
   mark(U42(U42(X187, X287, X338), X2, X3)) -> a__U42(a__U42(mark(X187), X287, X338), X2, X3) [2]
   mark(U42(plus(X188, X288), X2, X3)) -> a__U42(a__plus(mark(X188), mark(X288)), X2, X3) [2]
   mark(U42(tt, X2, X3)) -> a__U42(tt, X2, X3) [2]
   mark(U42(s(X96), X2, X3)) -> a__U42(s(mark(X96)), X2, X3) [2]
   mark(U42(0, X2, X3)) -> a__U42(0, X2, X3) [2]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(tt) -> tt [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(0) -> 0 [1]
   a__U11(X1, X2) -> U11(X1, X2) [1]
   a__U12(X) -> U12(X) [1]
   a__isNat(X) -> isNat(X) [1]
   a__U21(X) -> U21(X) [1]
   a__U31(X1, X2) -> U31(X1, X2) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__U42(X1, X2, X3) -> U42(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]

The TRS has the following type information:
a__U11 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
tt :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U12 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__isNat :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U21 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U31 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
mark :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U41 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U42 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
s :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__plus :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
0 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
plus :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U11 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U12 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
isNat :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U21 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U31 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U41 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U42 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42

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

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

   tt => 1
   0 => 0

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

(34)
Obligation:
Complexity RNTS consisting of the following rules:

   a__U11(z, z') -{ 2 }-> a__U12(a__U21(a__isNat(V1''))) :|: V1'' >= 0, z = 1, z' = 1 + V1''
   a__U11(z, z') -{ 2 }-> a__U12(a__U11(a__isNat(V1'), V2')) :|: z = 1, z' = 1 + V1' + V2', V2' >= 0, V1' >= 0
   a__U11(z, z') -{ 2 }-> a__U12(1) :|: z = 1, z' = 0
   a__U11(z, z') -{ 2 }-> a__U12(1 + V2) :|: z' = V2, z = 1, V2 >= 0
   a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U12(z) -{ 1 }-> 1 :|: z = 1
   a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U21(z) -{ 1 }-> 1 :|: z = 1
   a__U21(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U31(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0
   a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U41(z, z', z'') -{ 2 }-> a__U42(a__U21(a__isNat(V12)), M, 1 + V12) :|: z' = M, z = 1, z'' = 1 + V12, V12 >= 0, M >= 0
   a__U41(z, z', z'') -{ 2 }-> a__U42(a__U11(a__isNat(V11), V2''), M, 1 + V11 + V2'') :|: z' = M, V11 >= 0, V2'' >= 0, z = 1, z'' = 1 + V11 + V2'', M >= 0
   a__U41(z, z', z'') -{ 2 }-> a__U42(1, M, 0) :|: z'' = 0, z' = M, z = 1, M >= 0
   a__U41(z, z', z'') -{ 2 }-> a__U42(1 + N, M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   a__U41(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U42(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   a__U42(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__isNat(z) -{ 2 }-> a__U21(a__U21(a__isNat(V16))) :|: z = 1 + (1 + V16), V16 >= 0
   a__isNat(z) -{ 2 }-> a__U21(a__U11(a__isNat(V15), V22)) :|: z = 1 + (1 + V15 + V22), V22 >= 0, V15 >= 0
   a__isNat(z) -{ 2 }-> a__U21(1) :|: z = 1 + 0
   a__isNat(z) -{ 2 }-> a__U21(1 + V1) :|: z = 1 + V1, V1 >= 0
   a__isNat(z) -{ 2 }-> a__U11(a__U21(a__isNat(V14)), V2) :|: V14 >= 0, z = 1 + (1 + V14) + V2, V2 >= 0
   a__isNat(z) -{ 2 }-> a__U11(a__U11(a__isNat(V13), V21), V2) :|: V21 >= 0, V13 >= 0, V2 >= 0, z = 1 + (1 + V13 + V21) + V2
   a__isNat(z) -{ 2 }-> a__U11(1, V2) :|: V2 >= 0, z = 1 + 0 + V2
   a__isNat(z) -{ 2 }-> a__U11(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNat(z) -{ 1 }-> 1 :|: z = 0
   a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__plus(z, z') -{ 2 }-> a__U41(a__U21(a__isNat(V110)), 1 + V110, N) :|: V110 >= 0, z = N, z' = 1 + (1 + V110), N >= 0
   a__plus(z, z') -{ 2 }-> a__U41(a__U11(a__isNat(V19), V24), 1 + V19 + V24, N) :|: V24 >= 0, V19 >= 0, z = N, z' = 1 + (1 + V19 + V24), N >= 0
   a__plus(z, z') -{ 2 }-> a__U41(1, 0, N) :|: z = N, z' = 1 + 0, N >= 0
   a__plus(z, z') -{ 2 }-> a__U41(1 + M, M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0
   a__plus(z, z') -{ 2 }-> a__U31(a__U21(a__isNat(V18)), 1 + V18) :|: V18 >= 0, z = 1 + V18, z' = 0
   a__plus(z, z') -{ 2 }-> a__U31(a__U11(a__isNat(V17), V23), 1 + V17 + V23) :|: z = 1 + V17 + V23, V23 >= 0, V17 >= 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U31(1, 0) :|: z = 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U31(1 + N, N) :|: z = N, z' = 0, N >= 0
   a__plus(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 2 }-> a__U42(a__plus(mark(X188), mark(X288)), X2, X3) :|: z = 1 + (1 + X188 + X288) + X2 + X3, X288 >= 0, X3 >= 0, X188 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U42(a__isNat(X94), X2, X3) :|: z = 1 + (1 + X94) + X2 + X3, X3 >= 0, X2 >= 0, X94 >= 0
   mark(z) -{ 2 }-> a__U42(a__U42(mark(X187), X287, X338), X2, X3) :|: X187 >= 0, X3 >= 0, z = 1 + (1 + X187 + X287 + X338) + X2 + X3, X338 >= 0, X287 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U42(a__U41(mark(X186), X286, X337), X2, X3) :|: X286 >= 0, z = 1 + (1 + X186 + X286 + X337) + X2 + X3, X186 >= 0, X3 >= 0, X2 >= 0, X337 >= 0
   mark(z) -{ 2 }-> a__U42(a__U31(mark(X185), X285), X2, X3) :|: X285 >= 0, X185 >= 0, X3 >= 0, z = 1 + (1 + X185 + X285) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U42(a__U21(mark(X95)), X2, X3) :|: X95 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X95) + X2 + X3
   mark(z) -{ 2 }-> a__U42(a__U12(mark(X93)), X2, X3) :|: z = 1 + (1 + X93) + X2 + X3, X3 >= 0, X2 >= 0, X93 >= 0
   mark(z) -{ 2 }-> a__U42(a__U11(mark(X184), X284), X2, X3) :|: z = 1 + (1 + X184 + X284) + X2 + X3, X184 >= 0, X284 >= 0, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U42(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U42(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U42(1 + mark(X96), X2, X3) :|: X96 >= 0, z = 1 + (1 + X96) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__plus(mark(X183), mark(X283)), X2, X3) :|: X183 >= 0, X283 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X183 + X283) + X2 + X3
   mark(z) -{ 2 }-> a__U41(a__isNat(X90), X2, X3) :|: z = 1 + (1 + X90) + X2 + X3, X90 >= 0, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U42(mark(X182), X282, X336), X2, X3) :|: z = 1 + (1 + X182 + X282 + X336) + X2 + X3, X282 >= 0, X3 >= 0, X182 >= 0, X2 >= 0, X336 >= 0
   mark(z) -{ 2 }-> a__U41(a__U41(mark(X181), X281, X335), X2, X3) :|: X181 >= 0, X3 >= 0, z = 1 + (1 + X181 + X281 + X335) + X2 + X3, X335 >= 0, X281 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U31(mark(X180), X280), X2, X3) :|: X280 >= 0, X3 >= 0, z = 1 + (1 + X180 + X280) + X2 + X3, X2 >= 0, X180 >= 0
   mark(z) -{ 2 }-> a__U41(a__U21(mark(X91)), X2, X3) :|: z = 1 + (1 + X91) + X2 + X3, X91 >= 0, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U12(mark(X89)), X2, X3) :|: X89 >= 0, X3 >= 0, z = 1 + (1 + X89) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U11(mark(X179), X279), X2, X3) :|: X279 >= 0, X3 >= 0, z = 1 + (1 + X179 + X279) + X2 + X3, X2 >= 0, X179 >= 0
   mark(z) -{ 2 }-> a__U41(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(1 + mark(X92), X2, X3) :|: X92 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X92) + X2 + X3
   mark(z) -{ 2 }-> a__U31(a__plus(mark(X178), mark(X278)), X2) :|: z = 1 + (1 + X178 + X278) + X2, X2 >= 0, X178 >= 0, X278 >= 0
   mark(z) -{ 2 }-> a__U31(a__isNat(X86), X2) :|: X86 >= 0, z = 1 + (1 + X86) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__U42(mark(X177), X277, X334), X2) :|: X177 >= 0, z = 1 + (1 + X177 + X277 + X334) + X2, X334 >= 0, X2 >= 0, X277 >= 0
   mark(z) -{ 2 }-> a__U31(a__U41(mark(X176), X276, X333), X2) :|: X176 >= 0, X276 >= 0, X333 >= 0, X2 >= 0, z = 1 + (1 + X176 + X276 + X333) + X2
   mark(z) -{ 2 }-> a__U31(a__U31(mark(X175), X275), X2) :|: X275 >= 0, X175 >= 0, z = 1 + (1 + X175 + X275) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__U21(mark(X87)), X2) :|: X87 >= 0, X2 >= 0, z = 1 + (1 + X87) + X2
   mark(z) -{ 2 }-> a__U31(a__U12(mark(X85)), X2) :|: X85 >= 0, z = 1 + (1 + X85) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__U11(mark(X174), X274), X2) :|: X174 >= 0, X274 >= 0, z = 1 + (1 + X174 + X274) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(1, X2) :|: z = 1 + 1 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(0, X2) :|: z = 1 + 0 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(1 + mark(X88), X2) :|: z = 1 + (1 + X88) + X2, X88 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__plus(mark(X173), mark(X273))) :|: z = 1 + (1 + X173 + X273), X173 >= 0, X273 >= 0
   mark(z) -{ 2 }-> a__U21(a__isNat(X82)) :|: X82 >= 0, z = 1 + (1 + X82)
   mark(z) -{ 2 }-> a__U21(a__U42(mark(X172), X272, X332)) :|: X172 >= 0, X272 >= 0, z = 1 + (1 + X172 + X272 + X332), X332 >= 0
   mark(z) -{ 2 }-> a__U21(a__U41(mark(X171), X271, X331)) :|: X271 >= 0, z = 1 + (1 + X171 + X271 + X331), X331 >= 0, X171 >= 0
   mark(z) -{ 2 }-> a__U21(a__U31(mark(X170), X270)) :|: z = 1 + (1 + X170 + X270), X170 >= 0, X270 >= 0
   mark(z) -{ 2 }-> a__U21(a__U21(mark(X83))) :|: z = 1 + (1 + X83), X83 >= 0
   mark(z) -{ 2 }-> a__U21(a__U12(mark(X81))) :|: X81 >= 0, z = 1 + (1 + X81)
   mark(z) -{ 2 }-> a__U21(a__U11(mark(X169), X269)) :|: X269 >= 0, X169 >= 0, z = 1 + (1 + X169 + X269)
   mark(z) -{ 2 }-> a__U21(1) :|: z = 1 + 1
   mark(z) -{ 2 }-> a__U21(0) :|: z = 1 + 0
   mark(z) -{ 2 }-> a__U21(1 + mark(X84)) :|: z = 1 + (1 + X84), X84 >= 0
   mark(z) -{ 2 }-> a__U12(a__plus(mark(X168), mark(X268))) :|: X168 >= 0, X268 >= 0, z = 1 + (1 + X168 + X268)
   mark(z) -{ 2 }-> a__U12(a__isNat(X78)) :|: z = 1 + (1 + X78), X78 >= 0
   mark(z) -{ 2 }-> a__U12(a__U42(mark(X167), X267, X330)) :|: X267 >= 0, z = 1 + (1 + X167 + X267 + X330), X330 >= 0, X167 >= 0
   mark(z) -{ 2 }-> a__U12(a__U41(mark(X166), X266, X329)) :|: X166 >= 0, X329 >= 0, X266 >= 0, z = 1 + (1 + X166 + X266 + X329)
   mark(z) -{ 2 }-> a__U12(a__U31(mark(X165), X265)) :|: X265 >= 0, X165 >= 0, z = 1 + (1 + X165 + X265)
   mark(z) -{ 2 }-> a__U12(a__U21(mark(X79))) :|: X79 >= 0, z = 1 + (1 + X79)
   mark(z) -{ 2 }-> a__U12(a__U12(mark(X77))) :|: X77 >= 0, z = 1 + (1 + X77)
   mark(z) -{ 2 }-> a__U12(a__U11(mark(X164), X264)) :|: X264 >= 0, z = 1 + (1 + X164 + X264), X164 >= 0
   mark(z) -{ 2 }-> a__U12(1) :|: z = 1 + 1
   mark(z) -{ 2 }-> a__U12(0) :|: z = 1 + 0
   mark(z) -{ 2 }-> a__U12(1 + mark(X80)) :|: z = 1 + (1 + X80), X80 >= 0
   mark(z) -{ 2 }-> a__U11(a__plus(mark(X163), mark(X263)), X2) :|: X163 >= 0, z = 1 + (1 + X163 + X263) + X2, X263 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__isNat(X74), X2) :|: z = 1 + (1 + X74) + X2, X2 >= 0, X74 >= 0
   mark(z) -{ 2 }-> a__U11(a__U42(mark(X162), X262, X328), X2) :|: X162 >= 0, X262 >= 0, X328 >= 0, z = 1 + (1 + X162 + X262 + X328) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U41(mark(X161), X261, X327), X2) :|: X261 >= 0, z = 1 + (1 + X161 + X261 + X327) + X2, X327 >= 0, X2 >= 0, X161 >= 0
   mark(z) -{ 2 }-> a__U11(a__U31(mark(X160), X260), X2) :|: X160 >= 0, z = 1 + (1 + X160 + X260) + X2, X260 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U21(mark(X75)), X2) :|: X75 >= 0, z = 1 + (1 + X75) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U12(mark(X73)), X2) :|: X73 >= 0, z = 1 + (1 + X73) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U11(mark(X159), X259), X2) :|: X259 >= 0, z = 1 + (1 + X159 + X259) + X2, X2 >= 0, X159 >= 0
   mark(z) -{ 2 }-> a__U11(1, X2) :|: z = 1 + 1 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U11(0, X2) :|: z = 1 + 0 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U11(1 + mark(X76), X2) :|: X76 >= 0, X2 >= 0, z = 1 + (1 + X76) + X2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0


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

(35) InliningProof (UPPER BOUND(ID))
Inlined the following terminating rules on right-hand sides where appropriate:

   a__U12(z) -{ 1 }-> 1 :|: z = 1
   a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U21(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U21(z) -{ 1 }-> 1 :|: z = 1

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

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

   a__U11(z, z') -{ 2 }-> a__U12(a__U21(a__isNat(V1''))) :|: V1'' >= 0, z = 1, z' = 1 + V1''
   a__U11(z, z') -{ 2 }-> a__U12(a__U11(a__isNat(V1'), V2')) :|: z = 1, z' = 1 + V1' + V2', V2' >= 0, V1' >= 0
   a__U11(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1
   a__U11(z, z') -{ 3 }-> 1 :|: z' = V2, z = 1, V2 >= 0, 1 + V2 = 1
   a__U11(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X
   a__U11(z, z') -{ 3 }-> 1 + X :|: z' = V2, z = 1, V2 >= 0, X >= 0, 1 + V2 = X
   a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U12(z) -{ 1 }-> 1 :|: z = 1
   a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U21(z) -{ 1 }-> 1 :|: z = 1
   a__U21(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U31(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0
   a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U41(z, z', z'') -{ 2 }-> a__U42(a__U21(a__isNat(V12)), M, 1 + V12) :|: z' = M, z = 1, z'' = 1 + V12, V12 >= 0, M >= 0
   a__U41(z, z', z'') -{ 2 }-> a__U42(a__U11(a__isNat(V11), V2''), M, 1 + V11 + V2'') :|: z' = M, V11 >= 0, V2'' >= 0, z = 1, z'' = 1 + V11 + V2'', M >= 0
   a__U41(z, z', z'') -{ 2 }-> a__U42(1, M, 0) :|: z'' = 0, z' = M, z = 1, M >= 0
   a__U41(z, z', z'') -{ 2 }-> a__U42(1 + N, M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   a__U41(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U42(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   a__U42(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__isNat(z) -{ 2 }-> a__U21(a__U21(a__isNat(V16))) :|: z = 1 + (1 + V16), V16 >= 0
   a__isNat(z) -{ 2 }-> a__U21(a__U11(a__isNat(V15), V22)) :|: z = 1 + (1 + V15 + V22), V22 >= 0, V15 >= 0
   a__isNat(z) -{ 2 }-> a__U11(a__U21(a__isNat(V14)), V2) :|: V14 >= 0, z = 1 + (1 + V14) + V2, V2 >= 0
   a__isNat(z) -{ 2 }-> a__U11(a__U11(a__isNat(V13), V21), V2) :|: V21 >= 0, V13 >= 0, V2 >= 0, z = 1 + (1 + V13 + V21) + V2
   a__isNat(z) -{ 2 }-> a__U11(1, V2) :|: V2 >= 0, z = 1 + 0 + V2
   a__isNat(z) -{ 2 }-> a__U11(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNat(z) -{ 1 }-> 1 :|: z = 0
   a__isNat(z) -{ 3 }-> 1 :|: z = 1 + 0, 1 = 1
   a__isNat(z) -{ 3 }-> 1 :|: z = 1 + V1, V1 >= 0, 1 + V1 = 1
   a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__isNat(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 1 = X
   a__isNat(z) -{ 3 }-> 1 + X :|: z = 1 + V1, V1 >= 0, X >= 0, 1 + V1 = X
   a__plus(z, z') -{ 2 }-> a__U41(a__U21(a__isNat(V110)), 1 + V110, N) :|: V110 >= 0, z = N, z' = 1 + (1 + V110), N >= 0
   a__plus(z, z') -{ 2 }-> a__U41(a__U11(a__isNat(V19), V24), 1 + V19 + V24, N) :|: V24 >= 0, V19 >= 0, z = N, z' = 1 + (1 + V19 + V24), N >= 0
   a__plus(z, z') -{ 2 }-> a__U41(1, 0, N) :|: z = N, z' = 1 + 0, N >= 0
   a__plus(z, z') -{ 2 }-> a__U41(1 + M, M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0
   a__plus(z, z') -{ 2 }-> a__U31(a__U21(a__isNat(V18)), 1 + V18) :|: V18 >= 0, z = 1 + V18, z' = 0
   a__plus(z, z') -{ 2 }-> a__U31(a__U11(a__isNat(V17), V23), 1 + V17 + V23) :|: z = 1 + V17 + V23, V23 >= 0, V17 >= 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U31(1, 0) :|: z = 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U31(1 + N, N) :|: z = N, z' = 0, N >= 0
   a__plus(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 2 }-> a__U42(a__plus(mark(X188), mark(X288)), X2, X3) :|: z = 1 + (1 + X188 + X288) + X2 + X3, X288 >= 0, X3 >= 0, X188 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U42(a__isNat(X94), X2, X3) :|: z = 1 + (1 + X94) + X2 + X3, X3 >= 0, X2 >= 0, X94 >= 0
   mark(z) -{ 2 }-> a__U42(a__U42(mark(X187), X287, X338), X2, X3) :|: X187 >= 0, X3 >= 0, z = 1 + (1 + X187 + X287 + X338) + X2 + X3, X338 >= 0, X287 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U42(a__U41(mark(X186), X286, X337), X2, X3) :|: X286 >= 0, z = 1 + (1 + X186 + X286 + X337) + X2 + X3, X186 >= 0, X3 >= 0, X2 >= 0, X337 >= 0
   mark(z) -{ 2 }-> a__U42(a__U31(mark(X185), X285), X2, X3) :|: X285 >= 0, X185 >= 0, X3 >= 0, z = 1 + (1 + X185 + X285) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U42(a__U21(mark(X95)), X2, X3) :|: X95 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X95) + X2 + X3
   mark(z) -{ 2 }-> a__U42(a__U12(mark(X93)), X2, X3) :|: z = 1 + (1 + X93) + X2 + X3, X3 >= 0, X2 >= 0, X93 >= 0
   mark(z) -{ 2 }-> a__U42(a__U11(mark(X184), X284), X2, X3) :|: z = 1 + (1 + X184 + X284) + X2 + X3, X184 >= 0, X284 >= 0, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U42(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U42(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U42(1 + mark(X96), X2, X3) :|: X96 >= 0, z = 1 + (1 + X96) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__plus(mark(X183), mark(X283)), X2, X3) :|: X183 >= 0, X283 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X183 + X283) + X2 + X3
   mark(z) -{ 2 }-> a__U41(a__isNat(X90), X2, X3) :|: z = 1 + (1 + X90) + X2 + X3, X90 >= 0, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U42(mark(X182), X282, X336), X2, X3) :|: z = 1 + (1 + X182 + X282 + X336) + X2 + X3, X282 >= 0, X3 >= 0, X182 >= 0, X2 >= 0, X336 >= 0
   mark(z) -{ 2 }-> a__U41(a__U41(mark(X181), X281, X335), X2, X3) :|: X181 >= 0, X3 >= 0, z = 1 + (1 + X181 + X281 + X335) + X2 + X3, X335 >= 0, X281 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U31(mark(X180), X280), X2, X3) :|: X280 >= 0, X3 >= 0, z = 1 + (1 + X180 + X280) + X2 + X3, X2 >= 0, X180 >= 0
   mark(z) -{ 2 }-> a__U41(a__U21(mark(X91)), X2, X3) :|: z = 1 + (1 + X91) + X2 + X3, X91 >= 0, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U12(mark(X89)), X2, X3) :|: X89 >= 0, X3 >= 0, z = 1 + (1 + X89) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U11(mark(X179), X279), X2, X3) :|: X279 >= 0, X3 >= 0, z = 1 + (1 + X179 + X279) + X2 + X3, X2 >= 0, X179 >= 0
   mark(z) -{ 2 }-> a__U41(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(1 + mark(X92), X2, X3) :|: X92 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X92) + X2 + X3
   mark(z) -{ 2 }-> a__U31(a__plus(mark(X178), mark(X278)), X2) :|: z = 1 + (1 + X178 + X278) + X2, X2 >= 0, X178 >= 0, X278 >= 0
   mark(z) -{ 2 }-> a__U31(a__isNat(X86), X2) :|: X86 >= 0, z = 1 + (1 + X86) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__U42(mark(X177), X277, X334), X2) :|: X177 >= 0, z = 1 + (1 + X177 + X277 + X334) + X2, X334 >= 0, X2 >= 0, X277 >= 0
   mark(z) -{ 2 }-> a__U31(a__U41(mark(X176), X276, X333), X2) :|: X176 >= 0, X276 >= 0, X333 >= 0, X2 >= 0, z = 1 + (1 + X176 + X276 + X333) + X2
   mark(z) -{ 2 }-> a__U31(a__U31(mark(X175), X275), X2) :|: X275 >= 0, X175 >= 0, z = 1 + (1 + X175 + X275) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__U21(mark(X87)), X2) :|: X87 >= 0, X2 >= 0, z = 1 + (1 + X87) + X2
   mark(z) -{ 2 }-> a__U31(a__U12(mark(X85)), X2) :|: X85 >= 0, z = 1 + (1 + X85) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__U11(mark(X174), X274), X2) :|: X174 >= 0, X274 >= 0, z = 1 + (1 + X174 + X274) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(1, X2) :|: z = 1 + 1 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(0, X2) :|: z = 1 + 0 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(1 + mark(X88), X2) :|: z = 1 + (1 + X88) + X2, X88 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__plus(mark(X173), mark(X273))) :|: z = 1 + (1 + X173 + X273), X173 >= 0, X273 >= 0
   mark(z) -{ 2 }-> a__U21(a__isNat(X82)) :|: X82 >= 0, z = 1 + (1 + X82)
   mark(z) -{ 2 }-> a__U21(a__U42(mark(X172), X272, X332)) :|: X172 >= 0, X272 >= 0, z = 1 + (1 + X172 + X272 + X332), X332 >= 0
   mark(z) -{ 2 }-> a__U21(a__U41(mark(X171), X271, X331)) :|: X271 >= 0, z = 1 + (1 + X171 + X271 + X331), X331 >= 0, X171 >= 0
   mark(z) -{ 2 }-> a__U21(a__U31(mark(X170), X270)) :|: z = 1 + (1 + X170 + X270), X170 >= 0, X270 >= 0
   mark(z) -{ 2 }-> a__U21(a__U21(mark(X83))) :|: z = 1 + (1 + X83), X83 >= 0
   mark(z) -{ 2 }-> a__U21(a__U12(mark(X81))) :|: X81 >= 0, z = 1 + (1 + X81)
   mark(z) -{ 2 }-> a__U21(a__U11(mark(X169), X269)) :|: X269 >= 0, X169 >= 0, z = 1 + (1 + X169 + X269)
   mark(z) -{ 2 }-> a__U21(1 + mark(X84)) :|: z = 1 + (1 + X84), X84 >= 0
   mark(z) -{ 2 }-> a__U12(a__plus(mark(X168), mark(X268))) :|: X168 >= 0, X268 >= 0, z = 1 + (1 + X168 + X268)
   mark(z) -{ 2 }-> a__U12(a__isNat(X78)) :|: z = 1 + (1 + X78), X78 >= 0
   mark(z) -{ 2 }-> a__U12(a__U42(mark(X167), X267, X330)) :|: X267 >= 0, z = 1 + (1 + X167 + X267 + X330), X330 >= 0, X167 >= 0
   mark(z) -{ 2 }-> a__U12(a__U41(mark(X166), X266, X329)) :|: X166 >= 0, X329 >= 0, X266 >= 0, z = 1 + (1 + X166 + X266 + X329)
   mark(z) -{ 2 }-> a__U12(a__U31(mark(X165), X265)) :|: X265 >= 0, X165 >= 0, z = 1 + (1 + X165 + X265)
   mark(z) -{ 2 }-> a__U12(a__U21(mark(X79))) :|: X79 >= 0, z = 1 + (1 + X79)
   mark(z) -{ 2 }-> a__U12(a__U12(mark(X77))) :|: X77 >= 0, z = 1 + (1 + X77)
   mark(z) -{ 2 }-> a__U12(a__U11(mark(X164), X264)) :|: X264 >= 0, z = 1 + (1 + X164 + X264), X164 >= 0
   mark(z) -{ 2 }-> a__U12(1 + mark(X80)) :|: z = 1 + (1 + X80), X80 >= 0
   mark(z) -{ 2 }-> a__U11(a__plus(mark(X163), mark(X263)), X2) :|: X163 >= 0, z = 1 + (1 + X163 + X263) + X2, X263 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__isNat(X74), X2) :|: z = 1 + (1 + X74) + X2, X2 >= 0, X74 >= 0
   mark(z) -{ 2 }-> a__U11(a__U42(mark(X162), X262, X328), X2) :|: X162 >= 0, X262 >= 0, X328 >= 0, z = 1 + (1 + X162 + X262 + X328) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U41(mark(X161), X261, X327), X2) :|: X261 >= 0, z = 1 + (1 + X161 + X261 + X327) + X2, X327 >= 0, X2 >= 0, X161 >= 0
   mark(z) -{ 2 }-> a__U11(a__U31(mark(X160), X260), X2) :|: X160 >= 0, z = 1 + (1 + X160 + X260) + X2, X260 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U21(mark(X75)), X2) :|: X75 >= 0, z = 1 + (1 + X75) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U12(mark(X73)), X2) :|: X73 >= 0, z = 1 + (1 + X73) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U11(mark(X159), X259), X2) :|: X259 >= 0, z = 1 + (1 + X159 + X259) + X2, X2 >= 0, X159 >= 0
   mark(z) -{ 2 }-> a__U11(1, X2) :|: z = 1 + 1 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U11(0, X2) :|: z = 1 + 0 + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U11(1 + mark(X76), X2) :|: X76 >= 0, X2 >= 0, z = 1 + (1 + X76) + X2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 3 }-> 1 :|: z = 1 + 1, 1 = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 3 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   mark(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0


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

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

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

   a__U11(z, z') -{ 2 }-> a__U12(a__U21(a__isNat(z' - 1))) :|: z' - 1 >= 0, z = 1
   a__U11(z, z') -{ 2 }-> a__U12(a__U11(a__isNat(V1'), V2')) :|: z = 1, z' = 1 + V1' + V2', V2' >= 0, V1' >= 0
   a__U11(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1
   a__U11(z, z') -{ 3 }-> 1 :|: z = 1, z' >= 0, 1 + z' = 1
   a__U11(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X
   a__U11(z, z') -{ 3 }-> 1 + X :|: z = 1, z' >= 0, X >= 0, 1 + z' = X
   a__U11(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__U12(z) -{ 1 }-> 1 :|: z = 1
   a__U12(z) -{ 1 }-> 1 + z :|: z >= 0
   a__U21(z) -{ 1 }-> 1 :|: z = 1
   a__U21(z) -{ 1 }-> 1 + z :|: z >= 0
   a__U31(z, z') -{ 1 }-> mark(z') :|: z = 1, z' >= 0
   a__U31(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   a__U41(z, z', z'') -{ 2 }-> a__U42(a__U21(a__isNat(z'' - 1)), z', 1 + (z'' - 1)) :|: z = 1, z'' - 1 >= 0, z' >= 0
   a__U41(z, z', z'') -{ 2 }-> a__U42(a__U11(a__isNat(V11), V2''), z', 1 + V11 + V2'') :|: V11 >= 0, V2'' >= 0, z = 1, z'' = 1 + V11 + V2'', z' >= 0
   a__U41(z, z', z'') -{ 2 }-> a__U42(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   a__U41(z, z', z'') -{ 2 }-> a__U42(1 + z'', z', z'') :|: z = 1, z' >= 0, z'' >= 0
   a__U41(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0
   a__U42(z, z', z'') -{ 1 }-> 1 + a__plus(mark(z''), mark(z')) :|: z = 1, z' >= 0, z'' >= 0
   a__U42(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0
   a__isNat(z) -{ 2 }-> a__U21(a__U21(a__isNat(z - 2))) :|: z - 2 >= 0
   a__isNat(z) -{ 2 }-> a__U21(a__U11(a__isNat(V15), V22)) :|: z = 1 + (1 + V15 + V22), V22 >= 0, V15 >= 0
   a__isNat(z) -{ 2 }-> a__U11(a__U21(a__isNat(V14)), V2) :|: V14 >= 0, z = 1 + (1 + V14) + V2, V2 >= 0
   a__isNat(z) -{ 2 }-> a__U11(a__U11(a__isNat(V13), V21), V2) :|: V21 >= 0, V13 >= 0, V2 >= 0, z = 1 + (1 + V13 + V21) + V2
   a__isNat(z) -{ 2 }-> a__U11(1, z - 1) :|: z - 1 >= 0
   a__isNat(z) -{ 2 }-> a__U11(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNat(z) -{ 1 }-> 1 :|: z = 0
   a__isNat(z) -{ 3 }-> 1 :|: z = 1 + 0, 1 = 1
   a__isNat(z) -{ 3 }-> 1 :|: z - 1 >= 0, 1 + (z - 1) = 1
   a__isNat(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 1 = X
   a__isNat(z) -{ 3 }-> 1 + X :|: z - 1 >= 0, X >= 0, 1 + (z - 1) = X
   a__isNat(z) -{ 1 }-> 1 + z :|: z >= 0
   a__plus(z, z') -{ 2 }-> a__U41(a__U21(a__isNat(z' - 2)), 1 + (z' - 2), z) :|: z' - 2 >= 0, z >= 0
   a__plus(z, z') -{ 2 }-> a__U41(a__U11(a__isNat(V19), V24), 1 + V19 + V24, z) :|: V24 >= 0, V19 >= 0, z' = 1 + (1 + V19 + V24), z >= 0
   a__plus(z, z') -{ 2 }-> a__U41(1, 0, z) :|: z' = 1 + 0, z >= 0
   a__plus(z, z') -{ 2 }-> a__U41(1 + (z' - 1), z' - 1, z) :|: z' - 1 >= 0, z >= 0
   a__plus(z, z') -{ 2 }-> a__U31(a__U21(a__isNat(z - 1)), 1 + (z - 1)) :|: z - 1 >= 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U31(a__U11(a__isNat(V17), V23), 1 + V17 + V23) :|: z = 1 + V17 + V23, V23 >= 0, V17 >= 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U31(1, 0) :|: z = 0, z' = 0
   a__plus(z, z') -{ 2 }-> a__U31(1 + z, z) :|: z' = 0, z >= 0
   a__plus(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0
   mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__isNat(z - 1) :|: z - 1 >= 0
   mark(z) -{ 2 }-> a__U42(a__plus(mark(X188), mark(X288)), X2, X3) :|: z = 1 + (1 + X188 + X288) + X2 + X3, X288 >= 0, X3 >= 0, X188 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U42(a__isNat(X94), X2, X3) :|: z = 1 + (1 + X94) + X2 + X3, X3 >= 0, X2 >= 0, X94 >= 0
   mark(z) -{ 2 }-> a__U42(a__U42(mark(X187), X287, X338), X2, X3) :|: X187 >= 0, X3 >= 0, z = 1 + (1 + X187 + X287 + X338) + X2 + X3, X338 >= 0, X287 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U42(a__U41(mark(X186), X286, X337), X2, X3) :|: X286 >= 0, z = 1 + (1 + X186 + X286 + X337) + X2 + X3, X186 >= 0, X3 >= 0, X2 >= 0, X337 >= 0
   mark(z) -{ 2 }-> a__U42(a__U31(mark(X185), X285), X2, X3) :|: X285 >= 0, X185 >= 0, X3 >= 0, z = 1 + (1 + X185 + X285) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U42(a__U21(mark(X95)), X2, X3) :|: X95 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X95) + X2 + X3
   mark(z) -{ 2 }-> a__U42(a__U12(mark(X93)), X2, X3) :|: z = 1 + (1 + X93) + X2 + X3, X3 >= 0, X2 >= 0, X93 >= 0
   mark(z) -{ 2 }-> a__U42(a__U11(mark(X184), X284), X2, X3) :|: z = 1 + (1 + X184 + X284) + X2 + X3, X184 >= 0, X284 >= 0, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U42(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U42(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U42(1 + mark(X96), X2, X3) :|: X96 >= 0, z = 1 + (1 + X96) + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__plus(mark(X183), mark(X283)), X2, X3) :|: X183 >= 0, X283 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X183 + X283) + X2 + X3
   mark(z) -{ 2 }-> a__U41(a__isNat(X90), X2, X3) :|: z = 1 + (1 + X90) + X2 + X3, X90 >= 0, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U42(mark(X182), X282, X336), X2, X3) :|: z = 1 + (1 + X182 + X282 + X336) + X2 + X3, X282 >= 0, X3 >= 0, X182 >= 0, X2 >= 0, X336 >= 0
   mark(z) -{ 2 }-> a__U41(a__U41(mark(X181), X281, X335), X2, X3) :|: X181 >= 0, X3 >= 0, z = 1 + (1 + X181 + X281 + X335) + X2 + X3, X335 >= 0, X281 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U31(mark(X180), X280), X2, X3) :|: X280 >= 0, X3 >= 0, z = 1 + (1 + X180 + X280) + X2 + X3, X2 >= 0, X180 >= 0
   mark(z) -{ 2 }-> a__U41(a__U21(mark(X91)), X2, X3) :|: z = 1 + (1 + X91) + X2 + X3, X91 >= 0, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U12(mark(X89)), X2, X3) :|: X89 >= 0, X3 >= 0, z = 1 + (1 + X89) + X2 + X3, X2 >= 0
   mark(z) -{ 2 }-> a__U41(a__U11(mark(X179), X279), X2, X3) :|: X279 >= 0, X3 >= 0, z = 1 + (1 + X179 + X279) + X2 + X3, X2 >= 0, X179 >= 0
   mark(z) -{ 2 }-> a__U41(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U41(1 + mark(X92), X2, X3) :|: X92 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X92) + X2 + X3
   mark(z) -{ 2 }-> a__U31(a__plus(mark(X178), mark(X278)), X2) :|: z = 1 + (1 + X178 + X278) + X2, X2 >= 0, X178 >= 0, X278 >= 0
   mark(z) -{ 2 }-> a__U31(a__isNat(X86), X2) :|: X86 >= 0, z = 1 + (1 + X86) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__U42(mark(X177), X277, X334), X2) :|: X177 >= 0, z = 1 + (1 + X177 + X277 + X334) + X2, X334 >= 0, X2 >= 0, X277 >= 0
   mark(z) -{ 2 }-> a__U31(a__U41(mark(X176), X276, X333), X2) :|: X176 >= 0, X276 >= 0, X333 >= 0, X2 >= 0, z = 1 + (1 + X176 + X276 + X333) + X2
   mark(z) -{ 2 }-> a__U31(a__U31(mark(X175), X275), X2) :|: X275 >= 0, X175 >= 0, z = 1 + (1 + X175 + X275) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__U21(mark(X87)), X2) :|: X87 >= 0, X2 >= 0, z = 1 + (1 + X87) + X2
   mark(z) -{ 2 }-> a__U31(a__U12(mark(X85)), X2) :|: X85 >= 0, z = 1 + (1 + X85) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(a__U11(mark(X174), X274), X2) :|: X174 >= 0, X274 >= 0, z = 1 + (1 + X174 + X274) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U31(1, z - 2) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U31(0, z - 1) :|: z - 1 >= 0
   mark(z) -{ 2 }-> a__U31(1 + mark(X88), X2) :|: z = 1 + (1 + X88) + X2, X88 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U21(a__plus(mark(X173), mark(X273))) :|: z = 1 + (1 + X173 + X273), X173 >= 0, X273 >= 0
   mark(z) -{ 2 }-> a__U21(a__isNat(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U42(mark(X172), X272, X332)) :|: X172 >= 0, X272 >= 0, z = 1 + (1 + X172 + X272 + X332), X332 >= 0
   mark(z) -{ 2 }-> a__U21(a__U41(mark(X171), X271, X331)) :|: X271 >= 0, z = 1 + (1 + X171 + X271 + X331), X331 >= 0, X171 >= 0
   mark(z) -{ 2 }-> a__U21(a__U31(mark(X170), X270)) :|: z = 1 + (1 + X170 + X270), X170 >= 0, X270 >= 0
   mark(z) -{ 2 }-> a__U21(a__U21(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U12(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U21(a__U11(mark(X169), X269)) :|: X269 >= 0, X169 >= 0, z = 1 + (1 + X169 + X269)
   mark(z) -{ 2 }-> a__U21(1 + mark(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U12(a__plus(mark(X168), mark(X268))) :|: X168 >= 0, X268 >= 0, z = 1 + (1 + X168 + X268)
   mark(z) -{ 2 }-> a__U12(a__isNat(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U12(a__U42(mark(X167), X267, X330)) :|: X267 >= 0, z = 1 + (1 + X167 + X267 + X330), X330 >= 0, X167 >= 0
   mark(z) -{ 2 }-> a__U12(a__U41(mark(X166), X266, X329)) :|: X166 >= 0, X329 >= 0, X266 >= 0, z = 1 + (1 + X166 + X266 + X329)
   mark(z) -{ 2 }-> a__U12(a__U31(mark(X165), X265)) :|: X265 >= 0, X165 >= 0, z = 1 + (1 + X165 + X265)
   mark(z) -{ 2 }-> a__U12(a__U21(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U12(a__U12(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U12(a__U11(mark(X164), X264)) :|: X264 >= 0, z = 1 + (1 + X164 + X264), X164 >= 0
   mark(z) -{ 2 }-> a__U12(1 + mark(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U11(a__plus(mark(X163), mark(X263)), X2) :|: X163 >= 0, z = 1 + (1 + X163 + X263) + X2, X263 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__isNat(X74), X2) :|: z = 1 + (1 + X74) + X2, X2 >= 0, X74 >= 0
   mark(z) -{ 2 }-> a__U11(a__U42(mark(X162), X262, X328), X2) :|: X162 >= 0, X262 >= 0, X328 >= 0, z = 1 + (1 + X162 + X262 + X328) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U41(mark(X161), X261, X327), X2) :|: X261 >= 0, z = 1 + (1 + X161 + X261 + X327) + X2, X327 >= 0, X2 >= 0, X161 >= 0
   mark(z) -{ 2 }-> a__U11(a__U31(mark(X160), X260), X2) :|: X160 >= 0, z = 1 + (1 + X160 + X260) + X2, X260 >= 0, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U21(mark(X75)), X2) :|: X75 >= 0, z = 1 + (1 + X75) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U12(mark(X73)), X2) :|: X73 >= 0, z = 1 + (1 + X73) + X2, X2 >= 0
   mark(z) -{ 2 }-> a__U11(a__U11(mark(X159), X259), X2) :|: X259 >= 0, z = 1 + (1 + X159 + X259) + X2, X2 >= 0, X159 >= 0
   mark(z) -{ 2 }-> a__U11(1, z - 2) :|: z - 2 >= 0
   mark(z) -{ 2 }-> a__U11(0, z - 1) :|: z - 1 >= 0
   mark(z) -{ 2 }-> a__U11(1 + mark(X76), X2) :|: X76 >= 0, X2 >= 0, z = 1 + (1 + X76) + X2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 3 }-> 1 :|: z = 1 + 1, 1 = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 3 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X
   mark(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X
   mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0


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

(39) 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

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

(40)
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__U11(tt, V2) -> a__U12(a__isNat(V2)) [1]
   a__U12(tt) -> tt [1]
   a__U21(tt) -> tt [1]
   a__U31(tt, N) -> mark(N) [1]
   a__U41(tt, M, N) -> a__U42(a__isNat(N), M, N) [1]
   a__U42(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1]
   a__isNat(0) -> tt [1]
   a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) [1]
   a__isNat(s(V1)) -> a__U21(a__isNat(V1)) [1]
   a__plus(N, 0) -> a__U31(a__isNat(N), N) [1]
   a__plus(N, s(M)) -> a__U41(a__isNat(M), M, N) [1]
   mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1]
   mark(U12(X)) -> a__U12(mark(X)) [1]
   mark(isNat(X)) -> a__isNat(X) [1]
   mark(U21(X)) -> a__U21(mark(X)) [1]
   mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1]
   mark(U41(X1, X2, X3)) -> a__U41(mark(X1), X2, X3) [1]
   mark(U42(X1, X2, X3)) -> a__U42(mark(X1), X2, X3) [1]
   mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1]
   mark(tt) -> tt [1]
   mark(s(X)) -> s(mark(X)) [1]
   mark(0) -> 0 [1]
   a__U11(X1, X2) -> U11(X1, X2) [1]
   a__U12(X) -> U12(X) [1]
   a__isNat(X) -> isNat(X) [1]
   a__U21(X) -> U21(X) [1]
   a__U31(X1, X2) -> U31(X1, X2) [1]
   a__U41(X1, X2, X3) -> U41(X1, X2, X3) [1]
   a__U42(X1, X2, X3) -> U42(X1, X2, X3) [1]
   a__plus(X1, X2) -> plus(X1, X2) [1]

The TRS has the following type information:
a__U11 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
tt :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U12 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__isNat :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U21 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U31 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
mark :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U41 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__U42 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
s :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
a__plus :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
0 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
plus :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U11 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U12 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
isNat :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U21 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U31 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U41 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42
U42 :: tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42 -> tt:s:0:plus:U11:U12:isNat:U21:U31:U41:U42

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

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

   tt => 1
   0 => 0

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

(42)
Obligation:
Complexity RNTS consisting of the following rules:

   a__U11(z, z') -{ 1 }-> a__U12(a__isNat(V2)) :|: z' = V2, z = 1, V2 >= 0
   a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U12(z) -{ 1 }-> 1 :|: z = 1
   a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U21(z) -{ 1 }-> 1 :|: z = 1
   a__U21(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__U31(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0
   a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   a__U41(z, z', z'') -{ 1 }-> a__U42(a__isNat(N), M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   a__U41(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__U42(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0
   a__U42(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3
   a__isNat(z) -{ 1 }-> a__U21(a__isNat(V1)) :|: z = 1 + V1, V1 >= 0
   a__isNat(z) -{ 1 }-> a__U11(a__isNat(V1), V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2
   a__isNat(z) -{ 1 }-> 1 :|: z = 0
   a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X
   a__plus(z, z') -{ 1 }-> a__U41(a__isNat(M), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0
   a__plus(z, z') -{ 1 }-> a__U31(a__isNat(N), N) :|: z = N, z' = 0, N >= 0
   a__plus(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2
   mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U42(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> a__U41(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0
   mark(z) -{ 1 }-> a__U31(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> a__U21(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U12(mark(X)) :|: z = 1 + X, X >= 0
   mark(z) -{ 1 }-> a__U11(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2
   mark(z) -{ 1 }-> 1 :|: z = 1
   mark(z) -{ 1 }-> 0 :|: z = 0
   mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0

Only complete derivations are relevant for the runtime complexity.

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

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

(44)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0))
   A__U11(z0, z1) -> c1
   A__U12(tt) -> c2
   A__U12(z0) -> c3
   A__U21(tt) -> c4
   A__U21(z0) -> c5
   A__U31(tt, z0) -> c6(MARK(z0))
   A__U31(z0, z1) -> c7
   A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1))
   A__U41(z0, z1, z2) -> c9
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U42(z0, z1, z2) -> c12
   A__ISNAT(0) -> c13
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__U21(a__isNat(z0)), A__ISNAT(z0))
   A__ISNAT(z0) -> c16
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   A__PLUS(z0, z1) -> c19
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(U12(z0)) -> c21(A__U12(mark(z0)), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U21(z0)) -> c23(A__U21(mark(z0)), MARK(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(tt) -> c29
   MARK(s(z0)) -> c30(MARK(z0))
   MARK(0) -> c31
S tuples:
   A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0))
   A__U11(z0, z1) -> c1
   A__U12(tt) -> c2
   A__U12(z0) -> c3
   A__U21(tt) -> c4
   A__U21(z0) -> c5
   A__U31(tt, z0) -> c6(MARK(z0))
   A__U31(z0, z1) -> c7
   A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1))
   A__U41(z0, z1, z2) -> c9
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__U42(z0, z1, z2) -> c12
   A__ISNAT(0) -> c13
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__U21(a__isNat(z0)), A__ISNAT(z0))
   A__ISNAT(z0) -> c16
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   A__PLUS(z0, z1) -> c19
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(U12(z0)) -> c21(A__U12(mark(z0)), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U21(z0)) -> c23(A__U21(mark(z0)), MARK(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(tt) -> c29
   MARK(s(z0)) -> c30(MARK(z0))
   MARK(0) -> c31
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U11_2, A__U12_1, A__U21_1, A__U31_2, A__U41_3, A__U42_3, A__ISNAT_1, A__PLUS_2, MARK_1

Compound Symbols:   c_2, c1, c2, c3, c4, c5, c6_1, c7, c8_2, c9, c10_2, c11_2, c12, c13, c14_2, c15_2, c16, c17_2, c18_2, c19, c20_2, c21_2, c22_1, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c29, c30_1, c31


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

(45) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 13 trailing nodes:
   A__U42(z0, z1, z2) -> c12
   A__U12(z0) -> c3
   A__U21(z0) -> c5
   A__U12(tt) -> c2
   A__PLUS(z0, z1) -> c19
   A__U11(z0, z1) -> c1
   A__U41(z0, z1, z2) -> c9
   MARK(0) -> c31
   A__U31(z0, z1) -> c7
   MARK(tt) -> c29
   A__ISNAT(z0) -> c16
   A__U21(tt) -> c4
   A__ISNAT(0) -> c13

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

(46)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0))
   A__U31(tt, z0) -> c6(MARK(z0))
   A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1))
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__U21(a__isNat(z0)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(U12(z0)) -> c21(A__U12(mark(z0)), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U21(z0)) -> c23(A__U21(mark(z0)), MARK(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
S tuples:
   A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0))
   A__U31(tt, z0) -> c6(MARK(z0))
   A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1))
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__U21(a__isNat(z0)), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(U12(z0)) -> c21(A__U12(mark(z0)), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U21(z0)) -> c23(A__U21(mark(z0)), MARK(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U11_2, A__U31_2, A__U41_3, A__U42_3, A__ISNAT_1, A__PLUS_2, MARK_1

Compound Symbols:   c_2, c6_1, c8_2, c10_2, c11_2, c14_2, c15_2, c17_2, c18_2, c20_2, c21_2, c22_1, c23_2, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1


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

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

(48)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1))
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1))
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__U41_3, A__U42_3, A__ISNAT_1, A__PLUS_2, MARK_1, A__U11_2

Compound Symbols:   c6_1, c8_2, c10_2, c11_2, c14_2, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1


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

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

(50)
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__U31(tt, z0) -> c6(MARK(z0))
   A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1))
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))

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

   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0

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

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

(52)
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__U31(tt, z0) -> c6(MARK(z0))
   A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1))
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0

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

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

(54)
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__U31(tt, z0) -> c6(MARK(z0)) [1]
   A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1)) [1]
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1]
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) [1]
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) [1]
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) [1]
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) [1]
   MARK(isNat(z0)) -> c22(A__ISNAT(z0)) [1]
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) [1]
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(s(z0)) -> c30(MARK(z0)) [1]
   A__U11(tt, z0) -> c(A__ISNAT(z0)) [1]
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) [1]
   MARK(U12(z0)) -> c21(MARK(z0)) [1]
   MARK(U21(z0)) -> c23(MARK(z0)) [1]
   a__U11(tt, z0) -> a__U12(a__isNat(z0)) [0]
   a__U11(z0, z1) -> U11(z0, z1) [0]
   a__U12(tt) -> tt [0]
   a__U12(z0) -> U12(z0) [0]
   a__U21(tt) -> tt [0]
   a__U21(z0) -> U21(z0) [0]
   a__U31(tt, z0) -> mark(z0) [0]
   a__U31(z0, z1) -> U31(z0, z1) [0]
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) [0]
   a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0]
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0]
   a__U42(z0, z1, z2) -> U42(z0, z1, z2) [0]
   a__isNat(0) -> tt [0]
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) [0]
   a__isNat(s(z0)) -> a__U21(a__isNat(z0)) [0]
   a__isNat(z0) -> isNat(z0) [0]
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) [0]
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) [0]
   a__plus(z0, z1) -> plus(z0, z1) [0]
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0]
   mark(U12(z0)) -> a__U12(mark(z0)) [0]
   mark(isNat(z0)) -> a__isNat(z0) [0]
   mark(U21(z0)) -> a__U21(mark(z0)) [0]
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0]
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0]
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) [0]
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0]
   mark(tt) -> tt [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(0) -> 0 [0]

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

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

(56)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   A__U31(tt, z0) -> c6(MARK(z0)) [1]
   A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1)) [1]
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1]
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) [1]
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) [1]
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) [1]
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) [1]
   MARK(isNat(z0)) -> c22(A__ISNAT(z0)) [1]
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) [1]
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(s(z0)) -> c30(MARK(z0)) [1]
   A__U11(tt, z0) -> c(A__ISNAT(z0)) [1]
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) [1]
   MARK(U12(z0)) -> c21(MARK(z0)) [1]
   MARK(U21(z0)) -> c23(MARK(z0)) [1]
   a__U11(tt, z0) -> a__U12(a__isNat(z0)) [0]
   a__U11(z0, z1) -> U11(z0, z1) [0]
   a__U12(tt) -> tt [0]
   a__U12(z0) -> U12(z0) [0]
   a__U21(tt) -> tt [0]
   a__U21(z0) -> U21(z0) [0]
   a__U31(tt, z0) -> mark(z0) [0]
   a__U31(z0, z1) -> U31(z0, z1) [0]
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) [0]
   a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0]
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0]
   a__U42(z0, z1, z2) -> U42(z0, z1, z2) [0]
   a__isNat(0) -> tt [0]
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) [0]
   a__isNat(s(z0)) -> a__U21(a__isNat(z0)) [0]
   a__isNat(z0) -> isNat(z0) [0]
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) [0]
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) [0]
   a__plus(z0, z1) -> plus(z0, z1) [0]
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0]
   mark(U12(z0)) -> a__U12(mark(z0)) [0]
   mark(isNat(z0)) -> a__isNat(z0) [0]
   mark(U21(z0)) -> a__U21(mark(z0)) [0]
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0]
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0]
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) [0]
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0]
   mark(tt) -> tt [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(0) -> 0 [0]

The TRS has the following type information:
A__U31 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> c6
tt :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21
c6 :: c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c6
MARK :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
A__U41 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> c8
c8 :: c10:c11 -> c14:c15 -> c8
A__U42 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> c10:c11
a__isNat :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21
A__ISNAT :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> c14:c15
c10 :: c17:c18 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c10:c11
A__PLUS :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> c17:c18
mark :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21
c11 :: c17:c18 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c10:c11
plus :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21
c14 :: c -> c14:c15 -> c14:c15
A__U11 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> c
0 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21
c17 :: c6 -> c14:c15 -> c17:c18
s :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21
c18 :: c8 -> c14:c15 -> c17:c18
U11 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21
c20 :: c -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
isNat :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21
c22 :: c14:c15 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
U31 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21
c24 :: c6 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
U41 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21
c25 :: c8 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
U42 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21
c26 :: c10:c11 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
c27 :: c17:c18 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
c28 :: c17:c18 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
c30 :: c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
c :: c14:c15 -> c
c15 :: c14:c15 -> c14:c15
U12 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21
c21 :: c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
U21 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21
c23 :: c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
a__U11 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21
a__U12 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21
a__U21 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21
a__U31 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21
a__U41 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21
a__U42 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21
a__plus :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21 -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21

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

(57) 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__U31_2
   A__U41_3
   A__U42_3
   A__ISNAT_1
   A__PLUS_2
   MARK_1
   A__U11_2

(c) The following functions are completely defined:

   a__U11_2
   a__U12_1
   a__U21_1
   a__U31_2
   a__U41_3
   a__U42_3
   a__isNat_1
   a__plus_2
   mark_1

Due to the following rules being added:

   a__U11(v0, v1) -> null_a__U11 [0]
   a__U12(v0) -> null_a__U12 [0]
   a__U21(v0) -> null_a__U21 [0]
   a__U31(v0, v1) -> null_a__U31 [0]
   a__U41(v0, v1, v2) -> null_a__U41 [0]
   a__U42(v0, v1, v2) -> null_a__U42 [0]
   a__isNat(v0) -> null_a__isNat [0]
   a__plus(v0, v1) -> null_a__plus [0]
   mark(v0) -> null_mark [0]

And the following fresh constants:    null_a__U11, null_a__U12, null_a__U21, null_a__U31, null_a__U41, null_a__U42, null_a__isNat, null_a__plus, null_mark, const, const1, const2, const3, const4, const5, const6

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

(58)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

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

   A__U31(tt, z0) -> c6(MARK(z0)) [1]
   A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1)) [1]
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1]
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) [1]
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) [1]
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) [1]
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) [1]
   MARK(isNat(z0)) -> c22(A__ISNAT(z0)) [1]
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) [1]
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(s(z0)) -> c30(MARK(z0)) [1]
   A__U11(tt, z0) -> c(A__ISNAT(z0)) [1]
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) [1]
   MARK(U12(z0)) -> c21(MARK(z0)) [1]
   MARK(U21(z0)) -> c23(MARK(z0)) [1]
   a__U11(tt, z0) -> a__U12(a__isNat(z0)) [0]
   a__U11(z0, z1) -> U11(z0, z1) [0]
   a__U12(tt) -> tt [0]
   a__U12(z0) -> U12(z0) [0]
   a__U21(tt) -> tt [0]
   a__U21(z0) -> U21(z0) [0]
   a__U31(tt, z0) -> mark(z0) [0]
   a__U31(z0, z1) -> U31(z0, z1) [0]
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) [0]
   a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0]
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0]
   a__U42(z0, z1, z2) -> U42(z0, z1, z2) [0]
   a__isNat(0) -> tt [0]
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) [0]
   a__isNat(s(z0)) -> a__U21(a__isNat(z0)) [0]
   a__isNat(z0) -> isNat(z0) [0]
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) [0]
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) [0]
   a__plus(z0, z1) -> plus(z0, z1) [0]
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0]
   mark(U12(z0)) -> a__U12(mark(z0)) [0]
   mark(isNat(z0)) -> a__isNat(z0) [0]
   mark(U21(z0)) -> a__U21(mark(z0)) [0]
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0]
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0]
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) [0]
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0]
   mark(tt) -> tt [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(0) -> 0 [0]
   a__U11(v0, v1) -> null_a__U11 [0]
   a__U12(v0) -> null_a__U12 [0]
   a__U21(v0) -> null_a__U21 [0]
   a__U31(v0, v1) -> null_a__U31 [0]
   a__U41(v0, v1, v2) -> null_a__U41 [0]
   a__U42(v0, v1, v2) -> null_a__U42 [0]
   a__isNat(v0) -> null_a__isNat [0]
   a__plus(v0, v1) -> null_a__plus [0]
   mark(v0) -> null_mark [0]

The TRS has the following type information:
A__U31 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c6
tt :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c6 :: c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c6
MARK :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
A__U41 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c8
c8 :: c10:c11 -> c14:c15 -> c8
A__U42 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c10:c11
a__isNat :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
A__ISNAT :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c14:c15
c10 :: c17:c18 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c10:c11
A__PLUS :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c17:c18
mark :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c11 :: c17:c18 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c10:c11
plus :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c14 :: c -> c14:c15 -> c14:c15
A__U11 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c
0 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c17 :: c6 -> c14:c15 -> c17:c18
s :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c18 :: c8 -> c14:c15 -> c17:c18
U11 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c20 :: c -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
isNat :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c22 :: c14:c15 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
U31 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c24 :: c6 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
U41 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c25 :: c8 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
U42 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c26 :: c10:c11 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
c27 :: c17:c18 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
c28 :: c17:c18 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
c30 :: c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
c :: c14:c15 -> c
c15 :: c14:c15 -> c14:c15
U12 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c21 :: c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
U21 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c23 :: c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
a__U11 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
a__U12 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
a__U21 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
a__U31 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
a__U41 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
a__U42 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
a__plus :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__U11 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__U12 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__U21 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__U31 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__U41 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__U42 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__isNat :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__plus :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_mark :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
const :: c6
const1 :: c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
const2 :: c8
const3 :: c10:c11
const4 :: c14:c15
const5 :: c17:c18
const6 :: c

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

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

(60)
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__U31(tt, z0) -> c6(MARK(z0)) [1]
   A__U41(tt, z0, 0) -> c8(A__U42(tt, z0, 0), A__ISNAT(0)) [1]
   A__U41(tt, z0, plus(z0', z1')) -> c8(A__U42(a__U11(a__isNat(z0'), z1'), z0, plus(z0', z1')), A__ISNAT(plus(z0', z1'))) [1]
   A__U41(tt, z0, s(z0'')) -> c8(A__U42(a__U21(a__isNat(z0'')), z0, s(z0'')), A__ISNAT(s(z0''))) [1]
   A__U41(tt, z0, z1) -> c8(A__U42(isNat(z1), z0, z1), A__ISNAT(z1)) [1]
   A__U41(tt, z0, z1) -> c8(A__U42(null_a__isNat, z0, z1), A__ISNAT(z1)) [1]
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1]
   A__ISNAT(plus(0, z1)) -> c14(A__U11(tt, z1), A__ISNAT(0)) [1]
   A__ISNAT(plus(plus(z0235, z1130), z1)) -> c14(A__U11(a__U11(a__isNat(z0235), z1130), z1), A__ISNAT(plus(z0235, z1130))) [1]
   A__ISNAT(plus(s(z0236), z1)) -> c14(A__U11(a__U21(a__isNat(z0236)), z1), A__ISNAT(s(z0236))) [1]
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(isNat(z0), z1), A__ISNAT(z0)) [1]
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(null_a__isNat, z1), A__ISNAT(z0)) [1]
   A__PLUS(0, 0) -> c17(A__U31(tt, 0), A__ISNAT(0)) [1]
   A__PLUS(plus(z0237, z1131), 0) -> c17(A__U31(a__U11(a__isNat(z0237), z1131), plus(z0237, z1131)), A__ISNAT(plus(z0237, z1131))) [1]
   A__PLUS(s(z0238), 0) -> c17(A__U31(a__U21(a__isNat(z0238)), s(z0238)), A__ISNAT(s(z0238))) [1]
   A__PLUS(z0, 0) -> c17(A__U31(isNat(z0), z0), A__ISNAT(z0)) [1]
   A__PLUS(z0, 0) -> c17(A__U31(null_a__isNat, z0), A__ISNAT(z0)) [1]
   A__PLUS(z0, s(0)) -> c18(A__U41(tt, 0, z0), A__ISNAT(0)) [1]
   A__PLUS(z0, s(plus(z0239, z1132))) -> c18(A__U41(a__U11(a__isNat(z0239), z1132), plus(z0239, z1132), z0), A__ISNAT(plus(z0239, z1132))) [1]
   A__PLUS(z0, s(s(z0240))) -> c18(A__U41(a__U21(a__isNat(z0240)), s(z0240), z0), A__ISNAT(s(z0240))) [1]
   A__PLUS(z0, s(z1)) -> c18(A__U41(isNat(z1), z1, z0), A__ISNAT(z1)) [1]
   A__PLUS(z0, s(z1)) -> c18(A__U41(null_a__isNat, z1, z0), A__ISNAT(z1)) [1]
   MARK(U11(U11(z0241, z1133), z1)) -> c20(A__U11(a__U11(mark(z0241), z1133), z1), MARK(U11(z0241, z1133))) [1]
   MARK(U11(U12(z0242), z1)) -> c20(A__U11(a__U12(mark(z0242)), z1), MARK(U12(z0242))) [1]
   MARK(U11(isNat(z0243), z1)) -> c20(A__U11(a__isNat(z0243), z1), MARK(isNat(z0243))) [1]
   MARK(U11(U21(z0244), z1)) -> c20(A__U11(a__U21(mark(z0244)), z1), MARK(U21(z0244))) [1]
   MARK(U11(U31(z0245, z1134), z1)) -> c20(A__U11(a__U31(mark(z0245), z1134), z1), MARK(U31(z0245, z1134))) [1]
   MARK(U11(U41(z0246, z1135, z251), z1)) -> c20(A__U11(a__U41(mark(z0246), z1135, z251), z1), MARK(U41(z0246, z1135, z251))) [1]
   MARK(U11(U42(z0247, z1136, z252), z1)) -> c20(A__U11(a__U42(mark(z0247), z1136, z252), z1), MARK(U42(z0247, z1136, z252))) [1]
   MARK(U11(plus(z0248, z1137), z1)) -> c20(A__U11(a__plus(mark(z0248), mark(z1137)), z1), MARK(plus(z0248, z1137))) [1]
   MARK(U11(tt, z1)) -> c20(A__U11(tt, z1), MARK(tt)) [1]
   MARK(U11(s(z0249), z1)) -> c20(A__U11(s(mark(z0249)), z1), MARK(s(z0249))) [1]
   MARK(U11(0, z1)) -> c20(A__U11(0, z1), MARK(0)) [1]
   MARK(U11(z0, z1)) -> c20(A__U11(null_mark, z1), MARK(z0)) [1]
   MARK(isNat(z0)) -> c22(A__ISNAT(z0)) [1]
   MARK(U31(U11(z0250, z1138), z1)) -> c24(A__U31(a__U11(mark(z0250), z1138), z1), MARK(U11(z0250, z1138))) [1]
   MARK(U31(U12(z0251), z1)) -> c24(A__U31(a__U12(mark(z0251)), z1), MARK(U12(z0251))) [1]
   MARK(U31(isNat(z0252), z1)) -> c24(A__U31(a__isNat(z0252), z1), MARK(isNat(z0252))) [1]
   MARK(U31(U21(z0253), z1)) -> c24(A__U31(a__U21(mark(z0253)), z1), MARK(U21(z0253))) [1]
   MARK(U31(U31(z0254, z1139), z1)) -> c24(A__U31(a__U31(mark(z0254), z1139), z1), MARK(U31(z0254, z1139))) [1]
   MARK(U31(U41(z0255, z1140, z253), z1)) -> c24(A__U31(a__U41(mark(z0255), z1140, z253), z1), MARK(U41(z0255, z1140, z253))) [1]
   MARK(U31(U42(z0256, z1141, z254), z1)) -> c24(A__U31(a__U42(mark(z0256), z1141, z254), z1), MARK(U42(z0256, z1141, z254))) [1]
   MARK(U31(plus(z0257, z1142), z1)) -> c24(A__U31(a__plus(mark(z0257), mark(z1142)), z1), MARK(plus(z0257, z1142))) [1]
   MARK(U31(tt, z1)) -> c24(A__U31(tt, z1), MARK(tt)) [1]
   MARK(U31(s(z0258), z1)) -> c24(A__U31(s(mark(z0258)), z1), MARK(s(z0258))) [1]
   MARK(U31(0, z1)) -> c24(A__U31(0, z1), MARK(0)) [1]
   MARK(U31(z0, z1)) -> c24(A__U31(null_mark, z1), MARK(z0)) [1]
   MARK(U41(U11(z0259, z1143), z1, z2)) -> c25(A__U41(a__U11(mark(z0259), z1143), z1, z2), MARK(U11(z0259, z1143))) [1]
   MARK(U41(U12(z0260), z1, z2)) -> c25(A__U41(a__U12(mark(z0260)), z1, z2), MARK(U12(z0260))) [1]
   MARK(U41(isNat(z0261), z1, z2)) -> c25(A__U41(a__isNat(z0261), z1, z2), MARK(isNat(z0261))) [1]
   MARK(U41(U21(z0262), z1, z2)) -> c25(A__U41(a__U21(mark(z0262)), z1, z2), MARK(U21(z0262))) [1]
   MARK(U41(U31(z0263, z1144), z1, z2)) -> c25(A__U41(a__U31(mark(z0263), z1144), z1, z2), MARK(U31(z0263, z1144))) [1]
   MARK(U41(U41(z0264, z1145, z255), z1, z2)) -> c25(A__U41(a__U41(mark(z0264), z1145, z255), z1, z2), MARK(U41(z0264, z1145, z255))) [1]
   MARK(U41(U42(z0265, z1146, z256), z1, z2)) -> c25(A__U41(a__U42(mark(z0265), z1146, z256), z1, z2), MARK(U42(z0265, z1146, z256))) [1]
   MARK(U41(plus(z0266, z1147), z1, z2)) -> c25(A__U41(a__plus(mark(z0266), mark(z1147)), z1, z2), MARK(plus(z0266, z1147))) [1]
   MARK(U41(tt, z1, z2)) -> c25(A__U41(tt, z1, z2), MARK(tt)) [1]
   MARK(U41(s(z0267), z1, z2)) -> c25(A__U41(s(mark(z0267)), z1, z2), MARK(s(z0267))) [1]
   MARK(U41(0, z1, z2)) -> c25(A__U41(0, z1, z2), MARK(0)) [1]
   MARK(U41(z0, z1, z2)) -> c25(A__U41(null_mark, z1, z2), MARK(z0)) [1]
   MARK(U42(U11(z0268, z1148), z1, z2)) -> c26(A__U42(a__U11(mark(z0268), z1148), z1, z2), MARK(U11(z0268, z1148))) [1]
   MARK(U42(U12(z0269), z1, z2)) -> c26(A__U42(a__U12(mark(z0269)), z1, z2), MARK(U12(z0269))) [1]
   MARK(U42(isNat(z0270), z1, z2)) -> c26(A__U42(a__isNat(z0270), z1, z2), MARK(isNat(z0270))) [1]
   MARK(U42(U21(z0271), z1, z2)) -> c26(A__U42(a__U21(mark(z0271)), z1, z2), MARK(U21(z0271))) [1]
   MARK(U42(U31(z0272, z1149), z1, z2)) -> c26(A__U42(a__U31(mark(z0272), z1149), z1, z2), MARK(U31(z0272, z1149))) [1]
   MARK(U42(U41(z0273, z1150, z257), z1, z2)) -> c26(A__U42(a__U41(mark(z0273), z1150, z257), z1, z2), MARK(U41(z0273, z1150, z257))) [1]
   MARK(U42(U42(z0274, z1151, z258), z1, z2)) -> c26(A__U42(a__U42(mark(z0274), z1151, z258), z1, z2), MARK(U42(z0274, z1151, z258))) [1]
   MARK(U42(plus(z0275, z1152), z1, z2)) -> c26(A__U42(a__plus(mark(z0275), mark(z1152)), z1, z2), MARK(plus(z0275, z1152))) [1]
   MARK(U42(tt, z1, z2)) -> c26(A__U42(tt, z1, z2), MARK(tt)) [1]
   MARK(U42(s(z0276), z1, z2)) -> c26(A__U42(s(mark(z0276)), z1, z2), MARK(s(z0276))) [1]
   MARK(U42(0, z1, z2)) -> c26(A__U42(0, z1, z2), MARK(0)) [1]
   MARK(U42(z0, z1, z2)) -> c26(A__U42(null_mark, z1, z2), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(s(z0)) -> c30(MARK(z0)) [1]
   A__U11(tt, z0) -> c(A__ISNAT(z0)) [1]
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) [1]
   MARK(U12(z0)) -> c21(MARK(z0)) [1]
   MARK(U21(z0)) -> c23(MARK(z0)) [1]
   a__U11(tt, 0) -> a__U12(tt) [0]
   a__U11(tt, plus(z0511, z1283)) -> a__U12(a__U11(a__isNat(z0511), z1283)) [0]
   a__U11(tt, s(z0512)) -> a__U12(a__U21(a__isNat(z0512))) [0]
   a__U11(tt, z0) -> a__U12(isNat(z0)) [0]
   a__U11(tt, z0) -> a__U12(null_a__isNat) [0]
   a__U11(z0, z1) -> U11(z0, z1) [0]
   a__U12(tt) -> tt [0]
   a__U12(z0) -> U12(z0) [0]
   a__U21(tt) -> tt [0]
   a__U21(z0) -> U21(z0) [0]
   a__U31(tt, z0) -> mark(z0) [0]
   a__U31(z0, z1) -> U31(z0, z1) [0]
   a__U41(tt, z0, 0) -> a__U42(tt, z0, 0) [0]
   a__U41(tt, z0, plus(z0513, z1284)) -> a__U42(a__U11(a__isNat(z0513), z1284), z0, plus(z0513, z1284)) [0]
   a__U41(tt, z0, s(z0514)) -> a__U42(a__U21(a__isNat(z0514)), z0, s(z0514)) [0]
   a__U41(tt, z0, z1) -> a__U42(isNat(z1), z0, z1) [0]
   a__U41(tt, z0, z1) -> a__U42(null_a__isNat, z0, z1) [0]
   a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0]
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0]
   a__U42(z0, z1, z2) -> U42(z0, z1, z2) [0]
   a__isNat(0) -> tt [0]
   a__isNat(plus(0, z1)) -> a__U11(tt, z1) [0]
   a__isNat(plus(plus(z0632, z1350), z1)) -> a__U11(a__U11(a__isNat(z0632), z1350), z1) [0]
   a__isNat(plus(s(z0633), z1)) -> a__U11(a__U21(a__isNat(z0633)), z1) [0]
   a__isNat(plus(z0, z1)) -> a__U11(isNat(z0), z1) [0]
   a__isNat(plus(z0, z1)) -> a__U11(null_a__isNat, z1) [0]
   a__isNat(s(0)) -> a__U21(tt) [0]
   a__isNat(s(plus(z0634, z1351))) -> a__U21(a__U11(a__isNat(z0634), z1351)) [0]
   a__isNat(s(s(z0635))) -> a__U21(a__U21(a__isNat(z0635))) [0]
   a__isNat(s(z0)) -> a__U21(isNat(z0)) [0]
   a__isNat(s(z0)) -> a__U21(null_a__isNat) [0]
   a__isNat(z0) -> isNat(z0) [0]
   a__plus(0, 0) -> a__U31(tt, 0) [0]
   a__plus(plus(z0636, z1352), 0) -> a__U31(a__U11(a__isNat(z0636), z1352), plus(z0636, z1352)) [0]
   a__plus(s(z0637), 0) -> a__U31(a__U21(a__isNat(z0637)), s(z0637)) [0]
   a__plus(z0, 0) -> a__U31(isNat(z0), z0) [0]
   a__plus(z0, 0) -> a__U31(null_a__isNat, z0) [0]
   a__plus(z0, s(0)) -> a__U41(tt, 0, z0) [0]
   a__plus(z0, s(plus(z0638, z1353))) -> a__U41(a__U11(a__isNat(z0638), z1353), plus(z0638, z1353), z0) [0]
   a__plus(z0, s(s(z0639))) -> a__U41(a__U21(a__isNat(z0639)), s(z0639), z0) [0]
   a__plus(z0, s(z1)) -> a__U41(isNat(z1), z1, z0) [0]
   a__plus(z0, s(z1)) -> a__U41(null_a__isNat, z1, z0) [0]
   a__plus(z0, z1) -> plus(z0, z1) [0]
   mark(U11(U11(z0640, z1354), z1)) -> a__U11(a__U11(mark(z0640), z1354), z1) [0]
   mark(U11(U12(z0641), z1)) -> a__U11(a__U12(mark(z0641)), z1) [0]
   mark(U11(isNat(z0642), z1)) -> a__U11(a__isNat(z0642), z1) [0]
   mark(U11(U21(z0643), z1)) -> a__U11(a__U21(mark(z0643)), z1) [0]
   mark(U11(U31(z0644, z1355), z1)) -> a__U11(a__U31(mark(z0644), z1355), z1) [0]
   mark(U11(U41(z0645, z1356, z2137), z1)) -> a__U11(a__U41(mark(z0645), z1356, z2137), z1) [0]
   mark(U11(U42(z0646, z1357, z2138), z1)) -> a__U11(a__U42(mark(z0646), z1357, z2138), z1) [0]
   mark(U11(plus(z0647, z1358), z1)) -> a__U11(a__plus(mark(z0647), mark(z1358)), z1) [0]
   mark(U11(tt, z1)) -> a__U11(tt, z1) [0]
   mark(U11(s(z0648), z1)) -> a__U11(s(mark(z0648)), z1) [0]
   mark(U11(0, z1)) -> a__U11(0, z1) [0]
   mark(U11(z0, z1)) -> a__U11(null_mark, z1) [0]
   mark(U12(U11(z0649, z1359))) -> a__U12(a__U11(mark(z0649), z1359)) [0]
   mark(U12(U12(z0650))) -> a__U12(a__U12(mark(z0650))) [0]
   mark(U12(isNat(z0651))) -> a__U12(a__isNat(z0651)) [0]
   mark(U12(U21(z0652))) -> a__U12(a__U21(mark(z0652))) [0]
   mark(U12(U31(z0653, z1360))) -> a__U12(a__U31(mark(z0653), z1360)) [0]
   mark(U12(U41(z0654, z1361, z2139))) -> a__U12(a__U41(mark(z0654), z1361, z2139)) [0]
   mark(U12(U42(z0655, z1362, z2140))) -> a__U12(a__U42(mark(z0655), z1362, z2140)) [0]
   mark(U12(plus(z0656, z1363))) -> a__U12(a__plus(mark(z0656), mark(z1363))) [0]
   mark(U12(tt)) -> a__U12(tt) [0]
   mark(U12(s(z0657))) -> a__U12(s(mark(z0657))) [0]
   mark(U12(0)) -> a__U12(0) [0]
   mark(U12(z0)) -> a__U12(null_mark) [0]
   mark(isNat(z0)) -> a__isNat(z0) [0]
   mark(U21(U11(z0658, z1364))) -> a__U21(a__U11(mark(z0658), z1364)) [0]
   mark(U21(U12(z0659))) -> a__U21(a__U12(mark(z0659))) [0]
   mark(U21(isNat(z0660))) -> a__U21(a__isNat(z0660)) [0]
   mark(U21(U21(z0661))) -> a__U21(a__U21(mark(z0661))) [0]
   mark(U21(U31(z0662, z1365))) -> a__U21(a__U31(mark(z0662), z1365)) [0]
   mark(U21(U41(z0663, z1366, z2141))) -> a__U21(a__U41(mark(z0663), z1366, z2141)) [0]
   mark(U21(U42(z0664, z1367, z2142))) -> a__U21(a__U42(mark(z0664), z1367, z2142)) [0]
   mark(U21(plus(z0665, z1368))) -> a__U21(a__plus(mark(z0665), mark(z1368))) [0]
   mark(U21(tt)) -> a__U21(tt) [0]
   mark(U21(s(z0666))) -> a__U21(s(mark(z0666))) [0]
   mark(U21(0)) -> a__U21(0) [0]
   mark(U21(z0)) -> a__U21(null_mark) [0]
   mark(U31(U11(z0667, z1369), z1)) -> a__U31(a__U11(mark(z0667), z1369), z1) [0]
   mark(U31(U12(z0668), z1)) -> a__U31(a__U12(mark(z0668)), z1) [0]
   mark(U31(isNat(z0669), z1)) -> a__U31(a__isNat(z0669), z1) [0]
   mark(U31(U21(z0670), z1)) -> a__U31(a__U21(mark(z0670)), z1) [0]
   mark(U31(U31(z0671, z1370), z1)) -> a__U31(a__U31(mark(z0671), z1370), z1) [0]
   mark(U31(U41(z0672, z1371, z2143), z1)) -> a__U31(a__U41(mark(z0672), z1371, z2143), z1) [0]
   mark(U31(U42(z0673, z1372, z2144), z1)) -> a__U31(a__U42(mark(z0673), z1372, z2144), z1) [0]
   mark(U31(plus(z0674, z1373), z1)) -> a__U31(a__plus(mark(z0674), mark(z1373)), z1) [0]
   mark(U31(tt, z1)) -> a__U31(tt, z1) [0]
   mark(U31(s(z0675), z1)) -> a__U31(s(mark(z0675)), z1) [0]
   mark(U31(0, z1)) -> a__U31(0, z1) [0]
   mark(U31(z0, z1)) -> a__U31(null_mark, z1) [0]
   mark(U41(U11(z0676, z1374), z1, z2)) -> a__U41(a__U11(mark(z0676), z1374), z1, z2) [0]
   mark(U41(U12(z0677), z1, z2)) -> a__U41(a__U12(mark(z0677)), z1, z2) [0]
   mark(U41(isNat(z0678), z1, z2)) -> a__U41(a__isNat(z0678), z1, z2) [0]
   mark(U41(U21(z0679), z1, z2)) -> a__U41(a__U21(mark(z0679)), z1, z2) [0]
   mark(U41(U31(z0680, z1375), z1, z2)) -> a__U41(a__U31(mark(z0680), z1375), z1, z2) [0]
   mark(U41(U41(z0681, z1376, z2145), z1, z2)) -> a__U41(a__U41(mark(z0681), z1376, z2145), z1, z2) [0]
   mark(U41(U42(z0682, z1377, z2146), z1, z2)) -> a__U41(a__U42(mark(z0682), z1377, z2146), z1, z2) [0]
   mark(U41(plus(z0683, z1378), z1, z2)) -> a__U41(a__plus(mark(z0683), mark(z1378)), z1, z2) [0]
   mark(U41(tt, z1, z2)) -> a__U41(tt, z1, z2) [0]
   mark(U41(s(z0684), z1, z2)) -> a__U41(s(mark(z0684)), z1, z2) [0]
   mark(U41(0, z1, z2)) -> a__U41(0, z1, z2) [0]
   mark(U41(z0, z1, z2)) -> a__U41(null_mark, z1, z2) [0]
   mark(U42(U11(z0685, z1379), z1, z2)) -> a__U42(a__U11(mark(z0685), z1379), z1, z2) [0]
   mark(U42(U12(z0686), z1, z2)) -> a__U42(a__U12(mark(z0686)), z1, z2) [0]
   mark(U42(isNat(z0687), z1, z2)) -> a__U42(a__isNat(z0687), z1, z2) [0]
   mark(U42(U21(z0688), z1, z2)) -> a__U42(a__U21(mark(z0688)), z1, z2) [0]
   mark(U42(U31(z0689, z1380), z1, z2)) -> a__U42(a__U31(mark(z0689), z1380), z1, z2) [0]
   mark(U42(U41(z0690, z1381, z2147), z1, z2)) -> a__U42(a__U41(mark(z0690), z1381, z2147), z1, z2) [0]
   mark(U42(U42(z0691, z1382, z2148), z1, z2)) -> a__U42(a__U42(mark(z0691), z1382, z2148), z1, z2) [0]
   mark(U42(plus(z0692, z1383), z1, z2)) -> a__U42(a__plus(mark(z0692), mark(z1383)), z1, z2) [0]
   mark(U42(tt, z1, z2)) -> a__U42(tt, z1, z2) [0]
   mark(U42(s(z0693), z1, z2)) -> a__U42(s(mark(z0693)), z1, z2) [0]
   mark(U42(0, z1, z2)) -> a__U42(0, z1, z2) [0]
   mark(U42(z0, z1, z2)) -> a__U42(null_mark, z1, z2) [0]
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0]
   mark(tt) -> tt [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(0) -> 0 [0]
   a__U11(v0, v1) -> null_a__U11 [0]
   a__U12(v0) -> null_a__U12 [0]
   a__U21(v0) -> null_a__U21 [0]
   a__U31(v0, v1) -> null_a__U31 [0]
   a__U41(v0, v1, v2) -> null_a__U41 [0]
   a__U42(v0, v1, v2) -> null_a__U42 [0]
   a__isNat(v0) -> null_a__isNat [0]
   a__plus(v0, v1) -> null_a__plus [0]
   mark(v0) -> null_mark [0]

The TRS has the following type information:
A__U31 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c6
tt :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c6 :: c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c6
MARK :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
A__U41 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c8
c8 :: c10:c11 -> c14:c15 -> c8
A__U42 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c10:c11
a__isNat :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
A__ISNAT :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c14:c15
c10 :: c17:c18 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c10:c11
A__PLUS :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c17:c18
mark :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c11 :: c17:c18 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c10:c11
plus :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c14 :: c -> c14:c15 -> c14:c15
A__U11 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c
0 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c17 :: c6 -> c14:c15 -> c17:c18
s :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c18 :: c8 -> c14:c15 -> c17:c18
U11 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c20 :: c -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
isNat :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c22 :: c14:c15 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
U31 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c24 :: c6 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
U41 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c25 :: c8 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
U42 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c26 :: c10:c11 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
c27 :: c17:c18 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
c28 :: c17:c18 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
c30 :: c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
c :: c14:c15 -> c
c15 :: c14:c15 -> c14:c15
U12 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c21 :: c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
U21 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c23 :: c20:c22:c24:c25:c26:c27:c28:c30:c21:c23 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
a__U11 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
a__U12 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
a__U21 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
a__U31 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
a__U41 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
a__U42 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
a__plus :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__U11 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__U12 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__U21 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__U31 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__U41 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__U42 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__isNat :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__plus :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_mark :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
const :: c6
const1 :: c20:c22:c24:c25:c26:c27:c28:c30:c21:c23
const2 :: c8
const3 :: c10:c11
const4 :: c14:c15
const5 :: c17:c18
const6 :: c

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

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

   tt => 1
   0 => 0
   null_a__U11 => 0
   null_a__U12 => 0
   null_a__U21 => 0
   null_a__U31 => 0
   null_a__U41 => 0
   null_a__U42 => 0
   null_a__isNat => 0
   null_a__plus => 0
   null_mark => 0
   const => 0
   const1 => 0
   const2 => 0
   const3 => 0
   const4 => 0
   const5 => 0
   const6 => 0

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

(62)
Obligation:
Complexity RNTS consisting of the following rules:

   A__ISNAT(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__U21(a__isNat(z0236)), z1) + A__ISNAT(1 + z0236) :|: z1 >= 0, z = 1 + (1 + z0236) + z1, z0236 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__U11(a__isNat(z0235), z1130), z1) + A__ISNAT(1 + z0235 + z1130) :|: z0235 >= 0, z1130 >= 0, z = 1 + (1 + z0235 + z1130) + z1, z1 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(1, z1) + A__ISNAT(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(1 + z0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__PLUS(z, z') -{ 1 }-> 1 + A__U41(a__U21(a__isNat(z0240)), 1 + z0240, z0) + A__ISNAT(1 + z0240) :|: z = z0, z' = 1 + (1 + z0240), z0240 >= 0, z0 >= 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U41(a__U11(a__isNat(z0239), z1132), 1 + z0239 + z1132, z0) + A__ISNAT(1 + z0239 + z1132) :|: z0239 >= 0, z = z0, z' = 1 + (1 + z0239 + z1132), z1132 >= 0, z0 >= 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U41(1, 0, z0) + A__ISNAT(0) :|: z = z0, z' = 1 + 0, z0 >= 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U41(0, z1, z0) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   A__PLUS(z, z') -{ 1 }-> 1 + A__U41(1 + z1, z1, z0) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__U21(a__isNat(z0238)), 1 + z0238) + A__ISNAT(1 + z0238) :|: z0238 >= 0, z = 1 + z0238, z' = 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__U11(a__isNat(z0237), z1131), 1 + z0237 + z1131) + A__ISNAT(1 + z0237 + z1131) :|: z0237 >= 0, z = 1 + z0237 + z1131, z1131 >= 0, z' = 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U31(1, 0) + A__ISNAT(0) :|: z = 0, z' = 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U31(0, z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U31(1 + z0, z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0
   A__U11(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1, z0 >= 0, z' = z0
   A__U31(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 1, z0 >= 0, z' = z0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__U21(a__isNat(z0'')), z0, 1 + z0'') + A__ISNAT(1 + z0'') :|: z = 1, z'' = 1 + z0'', z0 >= 0, z0'' >= 0, z' = z0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__U11(a__isNat(z0'), z1'), z0, 1 + z0' + z1') + A__ISNAT(1 + z0' + z1') :|: z'' = 1 + z0' + z1', z = 1, z0' >= 0, z1' >= 0, z0 >= 0, z' = z0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(1, z0, 0) + A__ISNAT(0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(0, z0, z1) + A__ISNAT(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(1 + z1, z0, z1) + A__ISNAT(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U42(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U42(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__plus(mark(z0275), mark(z1152)), z1, z2) + MARK(1 + z0275 + z1152) :|: z1 >= 0, z = 1 + (1 + z0275 + z1152) + z1 + z2, z0275 >= 0, z1152 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__isNat(z0270), z1, z2) + MARK(1 + z0270) :|: z1 >= 0, z0270 >= 0, z = 1 + (1 + z0270) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__U42(mark(z0274), z1151, z258), z1, z2) + MARK(1 + z0274 + z1151 + z258) :|: z1151 >= 0, z258 >= 0, z1 >= 0, z = 1 + (1 + z0274 + z1151 + z258) + z1 + z2, z2 >= 0, z0274 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__U41(mark(z0273), z1150, z257), z1, z2) + MARK(1 + z0273 + z1150 + z257) :|: z0273 >= 0, z1 >= 0, z = 1 + (1 + z0273 + z1150 + z257) + z1 + z2, z257 >= 0, z1150 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__U31(mark(z0272), z1149), z1, z2) + MARK(1 + z0272 + z1149) :|: z1 >= 0, z0272 >= 0, z = 1 + (1 + z0272 + z1149) + z1 + z2, z1149 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__U21(mark(z0271)), z1, z2) + MARK(1 + z0271) :|: z = 1 + (1 + z0271) + z1 + z2, z1 >= 0, z0271 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__U12(mark(z0269)), z1, z2) + MARK(1 + z0269) :|: z1 >= 0, z0269 >= 0, z = 1 + (1 + z0269) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__U11(mark(z0268), z1148), z1, z2) + MARK(1 + z0268 + z1148) :|: z1 >= 0, z0268 >= 0, z = 1 + (1 + z0268 + z1148) + z1 + z2, z1148 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(1 + mark(z0276), z1, z2) + MARK(1 + z0276) :|: z1 >= 0, z0276 >= 0, z = 1 + (1 + z0276) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__plus(mark(z0266), mark(z1147)), z1, z2) + MARK(1 + z0266 + z1147) :|: z1 >= 0, z0266 >= 0, z = 1 + (1 + z0266 + z1147) + z1 + z2, z1147 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__isNat(z0261), z1, z2) + MARK(1 + z0261) :|: z = 1 + (1 + z0261) + z1 + z2, z1 >= 0, z0261 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__U42(mark(z0265), z1146, z256), z1, z2) + MARK(1 + z0265 + z1146 + z256) :|: z1 >= 0, z = 1 + (1 + z0265 + z1146 + z256) + z1 + z2, z256 >= 0, z1146 >= 0, z0265 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__U41(mark(z0264), z1145, z255), z1, z2) + MARK(1 + z0264 + z1145 + z255) :|: z1 >= 0, z1145 >= 0, z = 1 + (1 + z0264 + z1145 + z255) + z1 + z2, z0264 >= 0, z2 >= 0, z255 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__U31(mark(z0263), z1144), z1, z2) + MARK(1 + z0263 + z1144) :|: z0263 >= 0, z1 >= 0, z = 1 + (1 + z0263 + z1144) + z1 + z2, z1144 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__U21(mark(z0262)), z1, z2) + MARK(1 + z0262) :|: z = 1 + (1 + z0262) + z1 + z2, z0262 >= 0, z1 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__U12(mark(z0260)), z1, z2) + MARK(1 + z0260) :|: z1 >= 0, z0260 >= 0, z = 1 + (1 + z0260) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__U11(mark(z0259), z1143), z1, z2) + MARK(1 + z0259 + z1143) :|: z1 >= 0, z0259 >= 0, z = 1 + (1 + z0259 + z1143) + z1 + z2, z1143 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(1 + mark(z0267), z1, z2) + MARK(1 + z0267) :|: z1 >= 0, z0267 >= 0, z = 1 + (1 + z0267) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(a__plus(mark(z0257), mark(z1142)), z1) + MARK(1 + z0257 + z1142) :|: z1 >= 0, z0257 >= 0, z = 1 + (1 + z0257 + z1142) + z1, z1142 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(a__isNat(z0252), z1) + MARK(1 + z0252) :|: z0252 >= 0, z1 >= 0, z = 1 + (1 + z0252) + z1
   MARK(z) -{ 1 }-> 1 + A__U31(a__U42(mark(z0256), z1141, z254), z1) + MARK(1 + z0256 + z1141 + z254) :|: z0256 >= 0, z254 >= 0, z1 >= 0, z = 1 + (1 + z0256 + z1141 + z254) + z1, z1141 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(a__U41(mark(z0255), z1140, z253), z1) + MARK(1 + z0255 + z1140 + z253) :|: z1 >= 0, z253 >= 0, z0255 >= 0, z = 1 + (1 + z0255 + z1140 + z253) + z1, z1140 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(a__U31(mark(z0254), z1139), z1) + MARK(1 + z0254 + z1139) :|: z1 >= 0, z0254 >= 0, z = 1 + (1 + z0254 + z1139) + z1, z1139 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(a__U21(mark(z0253)), z1) + MARK(1 + z0253) :|: z1 >= 0, z0253 >= 0, z = 1 + (1 + z0253) + z1
   MARK(z) -{ 1 }-> 1 + A__U31(a__U12(mark(z0251)), z1) + MARK(1 + z0251) :|: z1 >= 0, z0251 >= 0, z = 1 + (1 + z0251) + z1
   MARK(z) -{ 1 }-> 1 + A__U31(a__U11(mark(z0250), z1138), z1) + MARK(1 + z0250 + z1138) :|: z1138 >= 0, z1 >= 0, z0250 >= 0, z = 1 + (1 + z0250 + z1138) + z1
   MARK(z) -{ 1 }-> 1 + A__U31(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1
   MARK(z) -{ 1 }-> 1 + A__U31(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U31(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1
   MARK(z) -{ 1 }-> 1 + A__U31(1 + mark(z0258), z1) + MARK(1 + z0258) :|: z = 1 + (1 + z0258) + z1, z1 >= 0, z0258 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__plus(mark(z0248), mark(z1137)), z1) + MARK(1 + z0248 + z1137) :|: z1 >= 0, z0248 >= 0, z1137 >= 0, z = 1 + (1 + z0248 + z1137) + z1
   MARK(z) -{ 1 }-> 1 + A__U11(a__isNat(z0243), z1) + MARK(1 + z0243) :|: z = 1 + (1 + z0243) + z1, z1 >= 0, z0243 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U42(mark(z0247), z1136, z252), z1) + MARK(1 + z0247 + z1136 + z252) :|: z1 >= 0, z = 1 + (1 + z0247 + z1136 + z252) + z1, z1136 >= 0, z252 >= 0, z0247 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U41(mark(z0246), z1135, z251), z1) + MARK(1 + z0246 + z1135 + z251) :|: z0246 >= 0, z1 >= 0, z1135 >= 0, z251 >= 0, z = 1 + (1 + z0246 + z1135 + z251) + z1
   MARK(z) -{ 1 }-> 1 + A__U11(a__U31(mark(z0245), z1134), z1) + MARK(1 + z0245 + z1134) :|: z1134 >= 0, z = 1 + (1 + z0245 + z1134) + z1, z1 >= 0, z0245 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U21(mark(z0244)), z1) + MARK(1 + z0244) :|: z1 >= 0, z = 1 + (1 + z0244) + z1, z0244 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U12(mark(z0242)), z1) + MARK(1 + z0242) :|: z0242 >= 0, z1 >= 0, z = 1 + (1 + z0242) + z1
   MARK(z) -{ 1 }-> 1 + A__U11(a__U11(mark(z0241), z1133), z1) + MARK(1 + z0241 + z1133) :|: z = 1 + (1 + z0241 + z1133) + z1, z1 >= 0, z1133 >= 0, z0241 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1
   MARK(z) -{ 1 }-> 1 + A__U11(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U11(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1
   MARK(z) -{ 1 }-> 1 + A__U11(1 + mark(z0249), z1) + MARK(1 + z0249) :|: z0249 >= 0, z1 >= 0, z = 1 + (1 + z0249) + z1
   MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__U11(z, z') -{ 0 }-> a__U12(a__U21(a__isNat(z0512))) :|: z = 1, z' = 1 + z0512, z0512 >= 0
   a__U11(z, z') -{ 0 }-> a__U12(a__U11(a__isNat(z0511), z1283)) :|: z' = 1 + z0511 + z1283, z = 1, z1283 >= 0, z0511 >= 0
   a__U11(z, z') -{ 0 }-> a__U12(1) :|: z = 1, z' = 0
   a__U11(z, z') -{ 0 }-> a__U12(0) :|: z = 1, z0 >= 0, z' = z0
   a__U11(z, z') -{ 0 }-> a__U12(1 + z0) :|: z = 1, z0 >= 0, z' = z0
   a__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U11(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U12(z) -{ 0 }-> 1 :|: z = 1
   a__U12(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U12(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U21(z) -{ 0 }-> 1 :|: z = 1
   a__U21(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U21(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U31(z, z') -{ 0 }-> mark(z0) :|: z = 1, z0 >= 0, z' = z0
   a__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U31(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U41(z, z', z'') -{ 0 }-> a__U42(a__U21(a__isNat(z0514)), z0, 1 + z0514) :|: z = 1, z0514 >= 0, z0 >= 0, z'' = 1 + z0514, z' = z0
   a__U41(z, z', z'') -{ 0 }-> a__U42(a__U11(a__isNat(z0513), z1284), z0, 1 + z0513 + z1284) :|: z = 1, z1284 >= 0, z0 >= 0, z0513 >= 0, z'' = 1 + z0513 + z1284, z' = z0
   a__U41(z, z', z'') -{ 0 }-> a__U42(1, z0, 0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0
   a__U41(z, z', z'') -{ 0 }-> a__U42(0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__U41(z, z', z'') -{ 0 }-> a__U42(1 + z1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__U41(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U41(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__U42(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U42(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z1), mark(z0)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__U42(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__isNat(z) -{ 0 }-> a__U21(a__U21(a__isNat(z0635))) :|: z0635 >= 0, z = 1 + (1 + z0635)
   a__isNat(z) -{ 0 }-> a__U21(a__U11(a__isNat(z0634), z1351)) :|: z0634 >= 0, z = 1 + (1 + z0634 + z1351), z1351 >= 0
   a__isNat(z) -{ 0 }-> a__U21(1) :|: z = 1 + 0
   a__isNat(z) -{ 0 }-> a__U21(0) :|: z = 1 + z0, z0 >= 0
   a__isNat(z) -{ 0 }-> a__U21(1 + z0) :|: z = 1 + z0, z0 >= 0
   a__isNat(z) -{ 0 }-> a__U11(a__U21(a__isNat(z0633)), z1) :|: z1 >= 0, z0633 >= 0, z = 1 + (1 + z0633) + z1
   a__isNat(z) -{ 0 }-> a__U11(a__U11(a__isNat(z0632), z1350), z1) :|: z1 >= 0, z0632 >= 0, z1350 >= 0, z = 1 + (1 + z0632 + z1350) + z1
   a__isNat(z) -{ 0 }-> a__U11(1, z1) :|: z1 >= 0, z = 1 + 0 + z1
   a__isNat(z) -{ 0 }-> a__U11(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNat(z) -{ 0 }-> a__U11(1 + z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNat(z) -{ 0 }-> 1 :|: z = 0
   a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__plus(z, z') -{ 0 }-> a__U41(a__U21(a__isNat(z0639)), 1 + z0639, z0) :|: z = z0, z0639 >= 0, z' = 1 + (1 + z0639), z0 >= 0
   a__plus(z, z') -{ 0 }-> a__U41(a__U11(a__isNat(z0638), z1353), 1 + z0638 + z1353, z0) :|: z1353 >= 0, z = z0, z' = 1 + (1 + z0638 + z1353), z0 >= 0, z0638 >= 0
   a__plus(z, z') -{ 0 }-> a__U41(1, 0, z0) :|: z = z0, z' = 1 + 0, z0 >= 0
   a__plus(z, z') -{ 0 }-> a__U41(0, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   a__plus(z, z') -{ 0 }-> a__U41(1 + z1, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   a__plus(z, z') -{ 0 }-> a__U31(a__U21(a__isNat(z0637)), 1 + z0637) :|: z = 1 + z0637, z0637 >= 0, z' = 0
   a__plus(z, z') -{ 0 }-> a__U31(a__U11(a__isNat(z0636), z1352), 1 + z0636 + z1352) :|: z = 1 + z0636 + z1352, z1352 >= 0, z0636 >= 0, z' = 0
   a__plus(z, z') -{ 0 }-> a__U31(1, 0) :|: z = 0, z' = 0
   a__plus(z, z') -{ 0 }-> a__U31(0, z0) :|: z = z0, z0 >= 0, z' = 0
   a__plus(z, z') -{ 0 }-> a__U31(1 + z0, z0) :|: z = z0, z0 >= 0, z' = 0
   a__plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__plus(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U42(a__plus(mark(z0692), mark(z1383)), z1, z2) :|: z1 >= 0, z1383 >= 0, z = 1 + (1 + z0692 + z1383) + z1 + z2, z0692 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__isNat(z0687), z1, z2) :|: z0687 >= 0, z = 1 + (1 + z0687) + z1 + z2, z1 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__U42(mark(z0691), z1382, z2148), z1, z2) :|: z1 >= 0, z2148 >= 0, z1382 >= 0, z = 1 + (1 + z0691 + z1382 + z2148) + z1 + z2, z0691 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__U41(mark(z0690), z1381, z2147), z1, z2) :|: z = 1 + (1 + z0690 + z1381 + z2147) + z1 + z2, z1 >= 0, z1381 >= 0, z2147 >= 0, z0690 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__U31(mark(z0689), z1380), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0689 + z1380) + z1 + z2, z1380 >= 0, z0689 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__U21(mark(z0688)), z1, z2) :|: z = 1 + (1 + z0688) + z1 + z2, z1 >= 0, z0688 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__U12(mark(z0686)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0686) + z1 + z2, z0686 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__U11(mark(z0685), z1379), z1, z2) :|: z1 >= 0, z1379 >= 0, z = 1 + (1 + z0685 + z1379) + z1 + z2, z0685 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U42(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U42(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(1 + mark(z0693), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0693) + z1 + z2, z0693 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U41(a__plus(mark(z0683), mark(z1378)), z1, z2) :|: z0683 >= 0, z1 >= 0, z1378 >= 0, z = 1 + (1 + z0683 + z1378) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U41(a__isNat(z0678), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0678) + z1 + z2, z0678 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U41(a__U42(mark(z0682), z1377, z2146), z1, z2) :|: z2146 >= 0, z1 >= 0, z0682 >= 0, z = 1 + (1 + z0682 + z1377 + z2146) + z1 + z2, z1377 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U41(a__U41(mark(z0681), z1376, z2145), z1, z2) :|: z1 >= 0, z0681 >= 0, z = 1 + (1 + z0681 + z1376 + z2145) + z1 + z2, z2145 >= 0, z2 >= 0, z1376 >= 0
   mark(z) -{ 0 }-> a__U41(a__U31(mark(z0680), z1375), z1, z2) :|: z1 >= 0, z0680 >= 0, z = 1 + (1 + z0680 + z1375) + z1 + z2, z1375 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U41(a__U21(mark(z0679)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0679) + z1 + z2, z0679 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U41(a__U12(mark(z0677)), z1, z2) :|: z1 >= 0, z0677 >= 0, z2 >= 0, z = 1 + (1 + z0677) + z1 + z2
   mark(z) -{ 0 }-> a__U41(a__U11(mark(z0676), z1374), z1, z2) :|: z0676 >= 0, z1 >= 0, z1374 >= 0, z = 1 + (1 + z0676 + z1374) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U41(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U41(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U41(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U41(1 + mark(z0684), z1, z2) :|: z1 >= 0, z0684 >= 0, z2 >= 0, z = 1 + (1 + z0684) + z1 + z2
   mark(z) -{ 0 }-> a__U31(a__plus(mark(z0674), mark(z1373)), z1) :|: z1 >= 0, z1373 >= 0, z0674 >= 0, z = 1 + (1 + z0674 + z1373) + z1
   mark(z) -{ 0 }-> a__U31(a__isNat(z0669), z1) :|: z1 >= 0, z = 1 + (1 + z0669) + z1, z0669 >= 0
   mark(z) -{ 0 }-> a__U31(a__U42(mark(z0673), z1372, z2144), z1) :|: z1 >= 0, z0673 >= 0, z1372 >= 0, z2144 >= 0, z = 1 + (1 + z0673 + z1372 + z2144) + z1
   mark(z) -{ 0 }-> a__U31(a__U41(mark(z0672), z1371, z2143), z1) :|: z0672 >= 0, z1 >= 0, z1371 >= 0, z = 1 + (1 + z0672 + z1371 + z2143) + z1, z2143 >= 0
   mark(z) -{ 0 }-> a__U31(a__U31(mark(z0671), z1370), z1) :|: z1 >= 0, z1370 >= 0, z = 1 + (1 + z0671 + z1370) + z1, z0671 >= 0
   mark(z) -{ 0 }-> a__U31(a__U21(mark(z0670)), z1) :|: z1 >= 0, z = 1 + (1 + z0670) + z1, z0670 >= 0
   mark(z) -{ 0 }-> a__U31(a__U12(mark(z0668)), z1) :|: z1 >= 0, z = 1 + (1 + z0668) + z1, z0668 >= 0
   mark(z) -{ 0 }-> a__U31(a__U11(mark(z0667), z1369), z1) :|: z1 >= 0, z = 1 + (1 + z0667 + z1369) + z1, z1369 >= 0, z0667 >= 0
   mark(z) -{ 0 }-> a__U31(1, z1) :|: z1 >= 0, z = 1 + 1 + z1
   mark(z) -{ 0 }-> a__U31(0, z1) :|: z1 >= 0, z = 1 + 0 + z1
   mark(z) -{ 0 }-> a__U31(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U31(1 + mark(z0675), z1) :|: z1 >= 0, z = 1 + (1 + z0675) + z1, z0675 >= 0
   mark(z) -{ 0 }-> a__U21(a__plus(mark(z0665), mark(z1368))) :|: z1368 >= 0, z0665 >= 0, z = 1 + (1 + z0665 + z1368)
   mark(z) -{ 0 }-> a__U21(a__isNat(z0660)) :|: z = 1 + (1 + z0660), z0660 >= 0
   mark(z) -{ 0 }-> a__U21(a__U42(mark(z0664), z1367, z2142)) :|: z = 1 + (1 + z0664 + z1367 + z2142), z1367 >= 0, z2142 >= 0, z0664 >= 0
   mark(z) -{ 0 }-> a__U21(a__U41(mark(z0663), z1366, z2141)) :|: z = 1 + (1 + z0663 + z1366 + z2141), z0663 >= 0, z2141 >= 0, z1366 >= 0
   mark(z) -{ 0 }-> a__U21(a__U31(mark(z0662), z1365)) :|: z0662 >= 0, z = 1 + (1 + z0662 + z1365), z1365 >= 0
   mark(z) -{ 0 }-> a__U21(a__U21(mark(z0661))) :|: z = 1 + (1 + z0661), z0661 >= 0
   mark(z) -{ 0 }-> a__U21(a__U12(mark(z0659))) :|: z = 1 + (1 + z0659), z0659 >= 0
   mark(z) -{ 0 }-> a__U21(a__U11(mark(z0658), z1364)) :|: z1364 >= 0, z = 1 + (1 + z0658 + z1364), z0658 >= 0
   mark(z) -{ 0 }-> a__U21(1) :|: z = 1 + 1
   mark(z) -{ 0 }-> a__U21(0) :|: z = 1 + 0
   mark(z) -{ 0 }-> a__U21(0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U21(1 + mark(z0666)) :|: z0666 >= 0, z = 1 + (1 + z0666)
   mark(z) -{ 0 }-> a__U12(a__plus(mark(z0656), mark(z1363))) :|: z1363 >= 0, z0656 >= 0, z = 1 + (1 + z0656 + z1363)
   mark(z) -{ 0 }-> a__U12(a__isNat(z0651)) :|: z0651 >= 0, z = 1 + (1 + z0651)
   mark(z) -{ 0 }-> a__U12(a__U42(mark(z0655), z1362, z2140)) :|: z0655 >= 0, z2140 >= 0, z1362 >= 0, z = 1 + (1 + z0655 + z1362 + z2140)
   mark(z) -{ 0 }-> a__U12(a__U41(mark(z0654), z1361, z2139)) :|: z = 1 + (1 + z0654 + z1361 + z2139), z2139 >= 0, z0654 >= 0, z1361 >= 0
   mark(z) -{ 0 }-> a__U12(a__U31(mark(z0653), z1360)) :|: z1360 >= 0, z0653 >= 0, z = 1 + (1 + z0653 + z1360)
   mark(z) -{ 0 }-> a__U12(a__U21(mark(z0652))) :|: z0652 >= 0, z = 1 + (1 + z0652)
   mark(z) -{ 0 }-> a__U12(a__U12(mark(z0650))) :|: z = 1 + (1 + z0650), z0650 >= 0
   mark(z) -{ 0 }-> a__U12(a__U11(mark(z0649), z1359)) :|: z0649 >= 0, z = 1 + (1 + z0649 + z1359), z1359 >= 0
   mark(z) -{ 0 }-> a__U12(1) :|: z = 1 + 1
   mark(z) -{ 0 }-> a__U12(0) :|: z = 1 + 0
   mark(z) -{ 0 }-> a__U12(0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U12(1 + mark(z0657)) :|: z = 1 + (1 + z0657), z0657 >= 0
   mark(z) -{ 0 }-> a__U11(a__plus(mark(z0647), mark(z1358)), z1) :|: z1 >= 0, z0647 >= 0, z = 1 + (1 + z0647 + z1358) + z1, z1358 >= 0
   mark(z) -{ 0 }-> a__U11(a__isNat(z0642), z1) :|: z = 1 + (1 + z0642) + z1, z1 >= 0, z0642 >= 0
   mark(z) -{ 0 }-> a__U11(a__U42(mark(z0646), z1357, z2138), z1) :|: z1357 >= 0, z1 >= 0, z = 1 + (1 + z0646 + z1357 + z2138) + z1, z2138 >= 0, z0646 >= 0
   mark(z) -{ 0 }-> a__U11(a__U41(mark(z0645), z1356, z2137), z1) :|: z = 1 + (1 + z0645 + z1356 + z2137) + z1, z0645 >= 0, z1 >= 0, z2137 >= 0, z1356 >= 0
   mark(z) -{ 0 }-> a__U11(a__U31(mark(z0644), z1355), z1) :|: z1 >= 0, z0644 >= 0, z1355 >= 0, z = 1 + (1 + z0644 + z1355) + z1
   mark(z) -{ 0 }-> a__U11(a__U21(mark(z0643)), z1) :|: z1 >= 0, z0643 >= 0, z = 1 + (1 + z0643) + z1
   mark(z) -{ 0 }-> a__U11(a__U12(mark(z0641)), z1) :|: z0641 >= 0, z1 >= 0, z = 1 + (1 + z0641) + z1
   mark(z) -{ 0 }-> a__U11(a__U11(mark(z0640), z1354), z1) :|: z1 >= 0, z1354 >= 0, z = 1 + (1 + z0640 + z1354) + z1, z0640 >= 0
   mark(z) -{ 0 }-> a__U11(1, z1) :|: z1 >= 0, z = 1 + 1 + z1
   mark(z) -{ 0 }-> a__U11(0, z1) :|: z1 >= 0, z = 1 + 0 + z1
   mark(z) -{ 0 }-> a__U11(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U11(1 + mark(z0648), z1) :|: z1 >= 0, z = 1 + (1 + z0648) + z1, z0648 >= 0
   mark(z) -{ 0 }-> 1 :|: z = 1
   mark(z) -{ 0 }-> 0 :|: z = 0
   mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0


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

(63) InliningProof (UPPER BOUND(ID))
Inlined the following terminating rules on right-hand sides where appropriate:

   a__U12(z) -{ 0 }-> 1 :|: z = 1
   a__U12(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U12(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U21(z) -{ 0 }-> 1 :|: z = 1
   a__U21(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U21(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0

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

(64)
Obligation:
Complexity RNTS consisting of the following rules:

   A__ISNAT(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__U21(a__isNat(z0236)), z1) + A__ISNAT(1 + z0236) :|: z1 >= 0, z = 1 + (1 + z0236) + z1, z0236 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__U11(a__isNat(z0235), z1130), z1) + A__ISNAT(1 + z0235 + z1130) :|: z0235 >= 0, z1130 >= 0, z = 1 + (1 + z0235 + z1130) + z1, z1 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(1, z1) + A__ISNAT(0) :|: z1 >= 0, z = 1 + 0 + z1
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(1 + z0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__PLUS(z, z') -{ 1 }-> 1 + A__U41(a__U21(a__isNat(z0240)), 1 + z0240, z0) + A__ISNAT(1 + z0240) :|: z = z0, z' = 1 + (1 + z0240), z0240 >= 0, z0 >= 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U41(a__U11(a__isNat(z0239), z1132), 1 + z0239 + z1132, z0) + A__ISNAT(1 + z0239 + z1132) :|: z0239 >= 0, z = z0, z' = 1 + (1 + z0239 + z1132), z1132 >= 0, z0 >= 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U41(1, 0, z0) + A__ISNAT(0) :|: z = z0, z' = 1 + 0, z0 >= 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U41(0, z1, z0) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   A__PLUS(z, z') -{ 1 }-> 1 + A__U41(1 + z1, z1, z0) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__U21(a__isNat(z0238)), 1 + z0238) + A__ISNAT(1 + z0238) :|: z0238 >= 0, z = 1 + z0238, z' = 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__U11(a__isNat(z0237), z1131), 1 + z0237 + z1131) + A__ISNAT(1 + z0237 + z1131) :|: z0237 >= 0, z = 1 + z0237 + z1131, z1131 >= 0, z' = 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U31(1, 0) + A__ISNAT(0) :|: z = 0, z' = 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U31(0, z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U31(1 + z0, z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0
   A__U11(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1, z0 >= 0, z' = z0
   A__U31(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 1, z0 >= 0, z' = z0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__U21(a__isNat(z0'')), z0, 1 + z0'') + A__ISNAT(1 + z0'') :|: z = 1, z'' = 1 + z0'', z0 >= 0, z0'' >= 0, z' = z0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__U11(a__isNat(z0'), z1'), z0, 1 + z0' + z1') + A__ISNAT(1 + z0' + z1') :|: z'' = 1 + z0' + z1', z = 1, z0' >= 0, z1' >= 0, z0 >= 0, z' = z0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(1, z0, 0) + A__ISNAT(0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(0, z0, z1) + A__ISNAT(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(1 + z1, z0, z1) + A__ISNAT(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U42(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U42(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__plus(mark(z0275), mark(z1152)), z1, z2) + MARK(1 + z0275 + z1152) :|: z1 >= 0, z = 1 + (1 + z0275 + z1152) + z1 + z2, z0275 >= 0, z1152 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__isNat(z0270), z1, z2) + MARK(1 + z0270) :|: z1 >= 0, z0270 >= 0, z = 1 + (1 + z0270) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__U42(mark(z0274), z1151, z258), z1, z2) + MARK(1 + z0274 + z1151 + z258) :|: z1151 >= 0, z258 >= 0, z1 >= 0, z = 1 + (1 + z0274 + z1151 + z258) + z1 + z2, z2 >= 0, z0274 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__U41(mark(z0273), z1150, z257), z1, z2) + MARK(1 + z0273 + z1150 + z257) :|: z0273 >= 0, z1 >= 0, z = 1 + (1 + z0273 + z1150 + z257) + z1 + z2, z257 >= 0, z1150 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__U31(mark(z0272), z1149), z1, z2) + MARK(1 + z0272 + z1149) :|: z1 >= 0, z0272 >= 0, z = 1 + (1 + z0272 + z1149) + z1 + z2, z1149 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__U21(mark(z0271)), z1, z2) + MARK(1 + z0271) :|: z = 1 + (1 + z0271) + z1 + z2, z1 >= 0, z0271 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__U12(mark(z0269)), z1, z2) + MARK(1 + z0269) :|: z1 >= 0, z0269 >= 0, z = 1 + (1 + z0269) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__U11(mark(z0268), z1148), z1, z2) + MARK(1 + z0268 + z1148) :|: z1 >= 0, z0268 >= 0, z = 1 + (1 + z0268 + z1148) + z1 + z2, z1148 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(1 + mark(z0276), z1, z2) + MARK(1 + z0276) :|: z1 >= 0, z0276 >= 0, z = 1 + (1 + z0276) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__plus(mark(z0266), mark(z1147)), z1, z2) + MARK(1 + z0266 + z1147) :|: z1 >= 0, z0266 >= 0, z = 1 + (1 + z0266 + z1147) + z1 + z2, z1147 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__isNat(z0261), z1, z2) + MARK(1 + z0261) :|: z = 1 + (1 + z0261) + z1 + z2, z1 >= 0, z0261 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__U42(mark(z0265), z1146, z256), z1, z2) + MARK(1 + z0265 + z1146 + z256) :|: z1 >= 0, z = 1 + (1 + z0265 + z1146 + z256) + z1 + z2, z256 >= 0, z1146 >= 0, z0265 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__U41(mark(z0264), z1145, z255), z1, z2) + MARK(1 + z0264 + z1145 + z255) :|: z1 >= 0, z1145 >= 0, z = 1 + (1 + z0264 + z1145 + z255) + z1 + z2, z0264 >= 0, z2 >= 0, z255 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__U31(mark(z0263), z1144), z1, z2) + MARK(1 + z0263 + z1144) :|: z0263 >= 0, z1 >= 0, z = 1 + (1 + z0263 + z1144) + z1 + z2, z1144 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__U21(mark(z0262)), z1, z2) + MARK(1 + z0262) :|: z = 1 + (1 + z0262) + z1 + z2, z0262 >= 0, z1 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__U12(mark(z0260)), z1, z2) + MARK(1 + z0260) :|: z1 >= 0, z0260 >= 0, z = 1 + (1 + z0260) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__U11(mark(z0259), z1143), z1, z2) + MARK(1 + z0259 + z1143) :|: z1 >= 0, z0259 >= 0, z = 1 + (1 + z0259 + z1143) + z1 + z2, z1143 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(1 + mark(z0267), z1, z2) + MARK(1 + z0267) :|: z1 >= 0, z0267 >= 0, z = 1 + (1 + z0267) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(a__plus(mark(z0257), mark(z1142)), z1) + MARK(1 + z0257 + z1142) :|: z1 >= 0, z0257 >= 0, z = 1 + (1 + z0257 + z1142) + z1, z1142 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(a__isNat(z0252), z1) + MARK(1 + z0252) :|: z0252 >= 0, z1 >= 0, z = 1 + (1 + z0252) + z1
   MARK(z) -{ 1 }-> 1 + A__U31(a__U42(mark(z0256), z1141, z254), z1) + MARK(1 + z0256 + z1141 + z254) :|: z0256 >= 0, z254 >= 0, z1 >= 0, z = 1 + (1 + z0256 + z1141 + z254) + z1, z1141 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(a__U41(mark(z0255), z1140, z253), z1) + MARK(1 + z0255 + z1140 + z253) :|: z1 >= 0, z253 >= 0, z0255 >= 0, z = 1 + (1 + z0255 + z1140 + z253) + z1, z1140 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(a__U31(mark(z0254), z1139), z1) + MARK(1 + z0254 + z1139) :|: z1 >= 0, z0254 >= 0, z = 1 + (1 + z0254 + z1139) + z1, z1139 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(a__U21(mark(z0253)), z1) + MARK(1 + z0253) :|: z1 >= 0, z0253 >= 0, z = 1 + (1 + z0253) + z1
   MARK(z) -{ 1 }-> 1 + A__U31(a__U12(mark(z0251)), z1) + MARK(1 + z0251) :|: z1 >= 0, z0251 >= 0, z = 1 + (1 + z0251) + z1
   MARK(z) -{ 1 }-> 1 + A__U31(a__U11(mark(z0250), z1138), z1) + MARK(1 + z0250 + z1138) :|: z1138 >= 0, z1 >= 0, z0250 >= 0, z = 1 + (1 + z0250 + z1138) + z1
   MARK(z) -{ 1 }-> 1 + A__U31(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1
   MARK(z) -{ 1 }-> 1 + A__U31(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U31(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1
   MARK(z) -{ 1 }-> 1 + A__U31(1 + mark(z0258), z1) + MARK(1 + z0258) :|: z = 1 + (1 + z0258) + z1, z1 >= 0, z0258 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__plus(mark(z0248), mark(z1137)), z1) + MARK(1 + z0248 + z1137) :|: z1 >= 0, z0248 >= 0, z1137 >= 0, z = 1 + (1 + z0248 + z1137) + z1
   MARK(z) -{ 1 }-> 1 + A__U11(a__isNat(z0243), z1) + MARK(1 + z0243) :|: z = 1 + (1 + z0243) + z1, z1 >= 0, z0243 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U42(mark(z0247), z1136, z252), z1) + MARK(1 + z0247 + z1136 + z252) :|: z1 >= 0, z = 1 + (1 + z0247 + z1136 + z252) + z1, z1136 >= 0, z252 >= 0, z0247 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U41(mark(z0246), z1135, z251), z1) + MARK(1 + z0246 + z1135 + z251) :|: z0246 >= 0, z1 >= 0, z1135 >= 0, z251 >= 0, z = 1 + (1 + z0246 + z1135 + z251) + z1
   MARK(z) -{ 1 }-> 1 + A__U11(a__U31(mark(z0245), z1134), z1) + MARK(1 + z0245 + z1134) :|: z1134 >= 0, z = 1 + (1 + z0245 + z1134) + z1, z1 >= 0, z0245 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U21(mark(z0244)), z1) + MARK(1 + z0244) :|: z1 >= 0, z = 1 + (1 + z0244) + z1, z0244 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U12(mark(z0242)), z1) + MARK(1 + z0242) :|: z0242 >= 0, z1 >= 0, z = 1 + (1 + z0242) + z1
   MARK(z) -{ 1 }-> 1 + A__U11(a__U11(mark(z0241), z1133), z1) + MARK(1 + z0241 + z1133) :|: z = 1 + (1 + z0241 + z1133) + z1, z1 >= 0, z1133 >= 0, z0241 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(1, z1) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1
   MARK(z) -{ 1 }-> 1 + A__U11(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U11(0, z1) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1
   MARK(z) -{ 1 }-> 1 + A__U11(1 + mark(z0249), z1) + MARK(1 + z0249) :|: z0249 >= 0, z1 >= 0, z = 1 + (1 + z0249) + z1
   MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__U11(z, z') -{ 0 }-> a__U12(a__U21(a__isNat(z0512))) :|: z = 1, z' = 1 + z0512, z0512 >= 0
   a__U11(z, z') -{ 0 }-> a__U12(a__U11(a__isNat(z0511), z1283)) :|: z' = 1 + z0511 + z1283, z = 1, z1283 >= 0, z0511 >= 0
   a__U11(z, z') -{ 0 }-> 1 :|: z = 1, z' = 0, 1 = 1
   a__U11(z, z') -{ 0 }-> 1 :|: z = 1, z0 >= 0, z' = z0, 1 + z0 = 1
   a__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U11(z, z') -{ 0 }-> 0 :|: z = 1, z' = 0, v0 >= 0, 1 = v0
   a__U11(z, z') -{ 0 }-> 0 :|: z = 1, z0 >= 0, z' = z0, v0 >= 0, 1 + z0 = v0
   a__U11(z, z') -{ 0 }-> 0 :|: z = 1, z0 >= 0, z' = z0, v0 >= 0, 0 = v0
   a__U11(z, z') -{ 0 }-> 1 + z0 :|: z = 1, z' = 0, 1 = z0, z0 >= 0
   a__U11(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z0 >= 0, z' = z0, 1 + z0 = z0', z0' >= 0
   a__U11(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z0 >= 0, z' = z0, 0 = z0', z0' >= 0
   a__U11(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U12(z) -{ 0 }-> 1 :|: z = 1
   a__U12(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U12(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U21(z) -{ 0 }-> 1 :|: z = 1
   a__U21(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U21(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U31(z, z') -{ 0 }-> mark(z0) :|: z = 1, z0 >= 0, z' = z0
   a__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U31(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U41(z, z', z'') -{ 0 }-> a__U42(a__U21(a__isNat(z0514)), z0, 1 + z0514) :|: z = 1, z0514 >= 0, z0 >= 0, z'' = 1 + z0514, z' = z0
   a__U41(z, z', z'') -{ 0 }-> a__U42(a__U11(a__isNat(z0513), z1284), z0, 1 + z0513 + z1284) :|: z = 1, z1284 >= 0, z0 >= 0, z0513 >= 0, z'' = 1 + z0513 + z1284, z' = z0
   a__U41(z, z', z'') -{ 0 }-> a__U42(1, z0, 0) :|: z'' = 0, z = 1, z0 >= 0, z' = z0
   a__U41(z, z', z'') -{ 0 }-> a__U42(0, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__U41(z, z', z'') -{ 0 }-> a__U42(1 + z1, z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__U41(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U41(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__U42(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U42(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z1), mark(z0)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__U42(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__isNat(z) -{ 0 }-> a__U21(a__U21(a__isNat(z0635))) :|: z0635 >= 0, z = 1 + (1 + z0635)
   a__isNat(z) -{ 0 }-> a__U21(a__U11(a__isNat(z0634), z1351)) :|: z0634 >= 0, z = 1 + (1 + z0634 + z1351), z1351 >= 0
   a__isNat(z) -{ 0 }-> a__U11(a__U21(a__isNat(z0633)), z1) :|: z1 >= 0, z0633 >= 0, z = 1 + (1 + z0633) + z1
   a__isNat(z) -{ 0 }-> a__U11(a__U11(a__isNat(z0632), z1350), z1) :|: z1 >= 0, z0632 >= 0, z1350 >= 0, z = 1 + (1 + z0632 + z1350) + z1
   a__isNat(z) -{ 0 }-> a__U11(1, z1) :|: z1 >= 0, z = 1 + 0 + z1
   a__isNat(z) -{ 0 }-> a__U11(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNat(z) -{ 0 }-> a__U11(1 + z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNat(z) -{ 0 }-> 1 :|: z = 0
   a__isNat(z) -{ 0 }-> 1 :|: z = 1 + 0, 1 = 1
   a__isNat(z) -{ 0 }-> 1 :|: z = 1 + z0, z0 >= 0, 1 + z0 = 1
   a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNat(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 1 = v0
   a__isNat(z) -{ 0 }-> 0 :|: z = 1 + z0, z0 >= 0, v0 >= 0, 1 + z0 = v0
   a__isNat(z) -{ 0 }-> 0 :|: z = 1 + z0, z0 >= 0, v0 >= 0, 0 = v0
   a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__isNat(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 1 = z0, z0 >= 0
   a__isNat(z) -{ 0 }-> 1 + z0' :|: z = 1 + z0, z0 >= 0, 1 + z0 = z0', z0' >= 0
   a__isNat(z) -{ 0 }-> 1 + z0' :|: z = 1 + z0, z0 >= 0, 0 = z0', z0' >= 0
   a__plus(z, z') -{ 0 }-> a__U41(a__U21(a__isNat(z0639)), 1 + z0639, z0) :|: z = z0, z0639 >= 0, z' = 1 + (1 + z0639), z0 >= 0
   a__plus(z, z') -{ 0 }-> a__U41(a__U11(a__isNat(z0638), z1353), 1 + z0638 + z1353, z0) :|: z1353 >= 0, z = z0, z' = 1 + (1 + z0638 + z1353), z0 >= 0, z0638 >= 0
   a__plus(z, z') -{ 0 }-> a__U41(1, 0, z0) :|: z = z0, z' = 1 + 0, z0 >= 0
   a__plus(z, z') -{ 0 }-> a__U41(0, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   a__plus(z, z') -{ 0 }-> a__U41(1 + z1, z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   a__plus(z, z') -{ 0 }-> a__U31(a__U21(a__isNat(z0637)), 1 + z0637) :|: z = 1 + z0637, z0637 >= 0, z' = 0
   a__plus(z, z') -{ 0 }-> a__U31(a__U11(a__isNat(z0636), z1352), 1 + z0636 + z1352) :|: z = 1 + z0636 + z1352, z1352 >= 0, z0636 >= 0, z' = 0
   a__plus(z, z') -{ 0 }-> a__U31(1, 0) :|: z = 0, z' = 0
   a__plus(z, z') -{ 0 }-> a__U31(0, z0) :|: z = z0, z0 >= 0, z' = 0
   a__plus(z, z') -{ 0 }-> a__U31(1 + z0, z0) :|: z = z0, z0 >= 0, z' = 0
   a__plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__plus(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U42(a__plus(mark(z0692), mark(z1383)), z1, z2) :|: z1 >= 0, z1383 >= 0, z = 1 + (1 + z0692 + z1383) + z1 + z2, z0692 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__isNat(z0687), z1, z2) :|: z0687 >= 0, z = 1 + (1 + z0687) + z1 + z2, z1 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__U42(mark(z0691), z1382, z2148), z1, z2) :|: z1 >= 0, z2148 >= 0, z1382 >= 0, z = 1 + (1 + z0691 + z1382 + z2148) + z1 + z2, z0691 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__U41(mark(z0690), z1381, z2147), z1, z2) :|: z = 1 + (1 + z0690 + z1381 + z2147) + z1 + z2, z1 >= 0, z1381 >= 0, z2147 >= 0, z0690 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__U31(mark(z0689), z1380), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0689 + z1380) + z1 + z2, z1380 >= 0, z0689 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__U21(mark(z0688)), z1, z2) :|: z = 1 + (1 + z0688) + z1 + z2, z1 >= 0, z0688 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__U12(mark(z0686)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0686) + z1 + z2, z0686 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__U11(mark(z0685), z1379), z1, z2) :|: z1 >= 0, z1379 >= 0, z = 1 + (1 + z0685 + z1379) + z1 + z2, z0685 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U42(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U42(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(1 + mark(z0693), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0693) + z1 + z2, z0693 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U41(a__plus(mark(z0683), mark(z1378)), z1, z2) :|: z0683 >= 0, z1 >= 0, z1378 >= 0, z = 1 + (1 + z0683 + z1378) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U41(a__isNat(z0678), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0678) + z1 + z2, z0678 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U41(a__U42(mark(z0682), z1377, z2146), z1, z2) :|: z2146 >= 0, z1 >= 0, z0682 >= 0, z = 1 + (1 + z0682 + z1377 + z2146) + z1 + z2, z1377 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U41(a__U41(mark(z0681), z1376, z2145), z1, z2) :|: z1 >= 0, z0681 >= 0, z = 1 + (1 + z0681 + z1376 + z2145) + z1 + z2, z2145 >= 0, z2 >= 0, z1376 >= 0
   mark(z) -{ 0 }-> a__U41(a__U31(mark(z0680), z1375), z1, z2) :|: z1 >= 0, z0680 >= 0, z = 1 + (1 + z0680 + z1375) + z1 + z2, z1375 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U41(a__U21(mark(z0679)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0679) + z1 + z2, z0679 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U41(a__U12(mark(z0677)), z1, z2) :|: z1 >= 0, z0677 >= 0, z2 >= 0, z = 1 + (1 + z0677) + z1 + z2
   mark(z) -{ 0 }-> a__U41(a__U11(mark(z0676), z1374), z1, z2) :|: z0676 >= 0, z1 >= 0, z1374 >= 0, z = 1 + (1 + z0676 + z1374) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U41(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U41(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U41(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U41(1 + mark(z0684), z1, z2) :|: z1 >= 0, z0684 >= 0, z2 >= 0, z = 1 + (1 + z0684) + z1 + z2
   mark(z) -{ 0 }-> a__U31(a__plus(mark(z0674), mark(z1373)), z1) :|: z1 >= 0, z1373 >= 0, z0674 >= 0, z = 1 + (1 + z0674 + z1373) + z1
   mark(z) -{ 0 }-> a__U31(a__isNat(z0669), z1) :|: z1 >= 0, z = 1 + (1 + z0669) + z1, z0669 >= 0
   mark(z) -{ 0 }-> a__U31(a__U42(mark(z0673), z1372, z2144), z1) :|: z1 >= 0, z0673 >= 0, z1372 >= 0, z2144 >= 0, z = 1 + (1 + z0673 + z1372 + z2144) + z1
   mark(z) -{ 0 }-> a__U31(a__U41(mark(z0672), z1371, z2143), z1) :|: z0672 >= 0, z1 >= 0, z1371 >= 0, z = 1 + (1 + z0672 + z1371 + z2143) + z1, z2143 >= 0
   mark(z) -{ 0 }-> a__U31(a__U31(mark(z0671), z1370), z1) :|: z1 >= 0, z1370 >= 0, z = 1 + (1 + z0671 + z1370) + z1, z0671 >= 0
   mark(z) -{ 0 }-> a__U31(a__U21(mark(z0670)), z1) :|: z1 >= 0, z = 1 + (1 + z0670) + z1, z0670 >= 0
   mark(z) -{ 0 }-> a__U31(a__U12(mark(z0668)), z1) :|: z1 >= 0, z = 1 + (1 + z0668) + z1, z0668 >= 0
   mark(z) -{ 0 }-> a__U31(a__U11(mark(z0667), z1369), z1) :|: z1 >= 0, z = 1 + (1 + z0667 + z1369) + z1, z1369 >= 0, z0667 >= 0
   mark(z) -{ 0 }-> a__U31(1, z1) :|: z1 >= 0, z = 1 + 1 + z1
   mark(z) -{ 0 }-> a__U31(0, z1) :|: z1 >= 0, z = 1 + 0 + z1
   mark(z) -{ 0 }-> a__U31(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U31(1 + mark(z0675), z1) :|: z1 >= 0, z = 1 + (1 + z0675) + z1, z0675 >= 0
   mark(z) -{ 0 }-> a__U21(a__plus(mark(z0665), mark(z1368))) :|: z1368 >= 0, z0665 >= 0, z = 1 + (1 + z0665 + z1368)
   mark(z) -{ 0 }-> a__U21(a__isNat(z0660)) :|: z = 1 + (1 + z0660), z0660 >= 0
   mark(z) -{ 0 }-> a__U21(a__U42(mark(z0664), z1367, z2142)) :|: z = 1 + (1 + z0664 + z1367 + z2142), z1367 >= 0, z2142 >= 0, z0664 >= 0
   mark(z) -{ 0 }-> a__U21(a__U41(mark(z0663), z1366, z2141)) :|: z = 1 + (1 + z0663 + z1366 + z2141), z0663 >= 0, z2141 >= 0, z1366 >= 0
   mark(z) -{ 0 }-> a__U21(a__U31(mark(z0662), z1365)) :|: z0662 >= 0, z = 1 + (1 + z0662 + z1365), z1365 >= 0
   mark(z) -{ 0 }-> a__U21(a__U21(mark(z0661))) :|: z = 1 + (1 + z0661), z0661 >= 0
   mark(z) -{ 0 }-> a__U21(a__U12(mark(z0659))) :|: z = 1 + (1 + z0659), z0659 >= 0
   mark(z) -{ 0 }-> a__U21(a__U11(mark(z0658), z1364)) :|: z1364 >= 0, z = 1 + (1 + z0658 + z1364), z0658 >= 0
   mark(z) -{ 0 }-> a__U21(1 + mark(z0666)) :|: z0666 >= 0, z = 1 + (1 + z0666)
   mark(z) -{ 0 }-> a__U12(a__plus(mark(z0656), mark(z1363))) :|: z1363 >= 0, z0656 >= 0, z = 1 + (1 + z0656 + z1363)
   mark(z) -{ 0 }-> a__U12(a__isNat(z0651)) :|: z0651 >= 0, z = 1 + (1 + z0651)
   mark(z) -{ 0 }-> a__U12(a__U42(mark(z0655), z1362, z2140)) :|: z0655 >= 0, z2140 >= 0, z1362 >= 0, z = 1 + (1 + z0655 + z1362 + z2140)
   mark(z) -{ 0 }-> a__U12(a__U41(mark(z0654), z1361, z2139)) :|: z = 1 + (1 + z0654 + z1361 + z2139), z2139 >= 0, z0654 >= 0, z1361 >= 0
   mark(z) -{ 0 }-> a__U12(a__U31(mark(z0653), z1360)) :|: z1360 >= 0, z0653 >= 0, z = 1 + (1 + z0653 + z1360)
   mark(z) -{ 0 }-> a__U12(a__U21(mark(z0652))) :|: z0652 >= 0, z = 1 + (1 + z0652)
   mark(z) -{ 0 }-> a__U12(a__U12(mark(z0650))) :|: z = 1 + (1 + z0650), z0650 >= 0
   mark(z) -{ 0 }-> a__U12(a__U11(mark(z0649), z1359)) :|: z0649 >= 0, z = 1 + (1 + z0649 + z1359), z1359 >= 0
   mark(z) -{ 0 }-> a__U12(1 + mark(z0657)) :|: z = 1 + (1 + z0657), z0657 >= 0
   mark(z) -{ 0 }-> a__U11(a__plus(mark(z0647), mark(z1358)), z1) :|: z1 >= 0, z0647 >= 0, z = 1 + (1 + z0647 + z1358) + z1, z1358 >= 0
   mark(z) -{ 0 }-> a__U11(a__isNat(z0642), z1) :|: z = 1 + (1 + z0642) + z1, z1 >= 0, z0642 >= 0
   mark(z) -{ 0 }-> a__U11(a__U42(mark(z0646), z1357, z2138), z1) :|: z1357 >= 0, z1 >= 0, z = 1 + (1 + z0646 + z1357 + z2138) + z1, z2138 >= 0, z0646 >= 0
   mark(z) -{ 0 }-> a__U11(a__U41(mark(z0645), z1356, z2137), z1) :|: z = 1 + (1 + z0645 + z1356 + z2137) + z1, z0645 >= 0, z1 >= 0, z2137 >= 0, z1356 >= 0
   mark(z) -{ 0 }-> a__U11(a__U31(mark(z0644), z1355), z1) :|: z1 >= 0, z0644 >= 0, z1355 >= 0, z = 1 + (1 + z0644 + z1355) + z1
   mark(z) -{ 0 }-> a__U11(a__U21(mark(z0643)), z1) :|: z1 >= 0, z0643 >= 0, z = 1 + (1 + z0643) + z1
   mark(z) -{ 0 }-> a__U11(a__U12(mark(z0641)), z1) :|: z0641 >= 0, z1 >= 0, z = 1 + (1 + z0641) + z1
   mark(z) -{ 0 }-> a__U11(a__U11(mark(z0640), z1354), z1) :|: z1 >= 0, z1354 >= 0, z = 1 + (1 + z0640 + z1354) + z1, z0640 >= 0
   mark(z) -{ 0 }-> a__U11(1, z1) :|: z1 >= 0, z = 1 + 1 + z1
   mark(z) -{ 0 }-> a__U11(0, z1) :|: z1 >= 0, z = 1 + 0 + z1
   mark(z) -{ 0 }-> a__U11(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U11(1 + mark(z0648), z1) :|: z1 >= 0, z = 1 + (1 + z0648) + z1, z0648 >= 0
   mark(z) -{ 0 }-> 1 :|: z = 1
   mark(z) -{ 0 }-> 1 :|: z = 1 + 1, 1 = 1
   mark(z) -{ 0 }-> 0 :|: z = 0
   mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   mark(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0
   mark(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   mark(z) -{ 0 }-> 0 :|: z = 1 + z0, z0 >= 0, v0 >= 0, 0 = v0
   mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 1, 1 = z0, z0 >= 0
   mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   mark(z) -{ 0 }-> 1 + z0' :|: z = 1 + z0, z0 >= 0, 0 = z0', z0' >= 0
   mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0


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

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

(66)
Obligation:
Complexity RNTS consisting of the following rules:

   A__ISNAT(z) -{ 1 }-> 1 + A__ISNAT(z - 1) :|: z - 1 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__U21(a__isNat(z0236)), z1) + A__ISNAT(1 + z0236) :|: z1 >= 0, z = 1 + (1 + z0236) + z1, z0236 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__U11(a__isNat(z0235), z1130), z1) + A__ISNAT(1 + z0235 + z1130) :|: z0235 >= 0, z1130 >= 0, z = 1 + (1 + z0235 + z1130) + z1, z1 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(1, z - 1) + A__ISNAT(0) :|: z - 1 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(1 + z0, z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__PLUS(z, z') -{ 1 }-> 1 + A__U41(a__U21(a__isNat(z' - 2)), 1 + (z' - 2), z) + A__ISNAT(1 + (z' - 2)) :|: z' - 2 >= 0, z >= 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U41(a__U11(a__isNat(z0239), z1132), 1 + z0239 + z1132, z) + A__ISNAT(1 + z0239 + z1132) :|: z0239 >= 0, z' = 1 + (1 + z0239 + z1132), z1132 >= 0, z >= 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U41(1, 0, z) + A__ISNAT(0) :|: z' = 1 + 0, z >= 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U41(0, z' - 1, z) + A__ISNAT(z' - 1) :|: z' - 1 >= 0, z >= 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U41(1 + (z' - 1), z' - 1, z) + A__ISNAT(z' - 1) :|: z' - 1 >= 0, z >= 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__U21(a__isNat(z - 1)), 1 + (z - 1)) + A__ISNAT(1 + (z - 1)) :|: z - 1 >= 0, z' = 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__U11(a__isNat(z0237), z1131), 1 + z0237 + z1131) + A__ISNAT(1 + z0237 + z1131) :|: z0237 >= 0, z = 1 + z0237 + z1131, z1131 >= 0, z' = 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U31(1, 0) + A__ISNAT(0) :|: z = 0, z' = 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U31(0, z) + A__ISNAT(z) :|: z >= 0, z' = 0
   A__PLUS(z, z') -{ 1 }-> 1 + A__U31(1 + z, z) + A__ISNAT(z) :|: z >= 0, z' = 0
   A__U11(z, z') -{ 1 }-> 1 + A__ISNAT(z') :|: z = 1, z' >= 0
   A__U31(z, z') -{ 1 }-> 1 + MARK(z') :|: z = 1, z' >= 0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__U21(a__isNat(z'' - 1)), z', 1 + (z'' - 1)) + A__ISNAT(1 + (z'' - 1)) :|: z = 1, z' >= 0, z'' - 1 >= 0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__U11(a__isNat(z0'), z1'), z', 1 + z0' + z1') + A__ISNAT(1 + z0' + z1') :|: z'' = 1 + z0' + z1', z = 1, z0' >= 0, z1' >= 0, z' >= 0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(1, z', 0) + A__ISNAT(0) :|: z'' = 0, z = 1, z' >= 0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(0, z', z'') + A__ISNAT(z'') :|: z'' >= 0, z = 1, z' >= 0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(1 + z'', z', z'') + A__ISNAT(z'') :|: z'' >= 0, z = 1, z' >= 0
   A__U42(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z''), mark(z')) + MARK(z') :|: z'' >= 0, z = 1, z' >= 0
   A__U42(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z''), mark(z')) + MARK(z'') :|: z'' >= 0, z = 1, z' >= 0
   MARK(z) -{ 1 }-> 1 + MARK(z - 1) :|: z - 1 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNAT(z - 1) :|: z - 1 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__plus(mark(z0275), mark(z1152)), z1, z2) + MARK(1 + z0275 + z1152) :|: z1 >= 0, z = 1 + (1 + z0275 + z1152) + z1 + z2, z0275 >= 0, z1152 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__isNat(z0270), z1, z2) + MARK(1 + z0270) :|: z1 >= 0, z0270 >= 0, z = 1 + (1 + z0270) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__U42(mark(z0274), z1151, z258), z1, z2) + MARK(1 + z0274 + z1151 + z258) :|: z1151 >= 0, z258 >= 0, z1 >= 0, z = 1 + (1 + z0274 + z1151 + z258) + z1 + z2, z2 >= 0, z0274 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__U41(mark(z0273), z1150, z257), z1, z2) + MARK(1 + z0273 + z1150 + z257) :|: z0273 >= 0, z1 >= 0, z = 1 + (1 + z0273 + z1150 + z257) + z1 + z2, z257 >= 0, z1150 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__U31(mark(z0272), z1149), z1, z2) + MARK(1 + z0272 + z1149) :|: z1 >= 0, z0272 >= 0, z = 1 + (1 + z0272 + z1149) + z1 + z2, z1149 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__U21(mark(z0271)), z1, z2) + MARK(1 + z0271) :|: z = 1 + (1 + z0271) + z1 + z2, z1 >= 0, z0271 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__U12(mark(z0269)), z1, z2) + MARK(1 + z0269) :|: z1 >= 0, z0269 >= 0, z = 1 + (1 + z0269) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(a__U11(mark(z0268), z1148), z1, z2) + MARK(1 + z0268 + z1148) :|: z1 >= 0, z0268 >= 0, z = 1 + (1 + z0268 + z1148) + z1 + z2, z1148 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(1 + mark(z0276), z1, z2) + MARK(1 + z0276) :|: z1 >= 0, z0276 >= 0, z = 1 + (1 + z0276) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__plus(mark(z0266), mark(z1147)), z1, z2) + MARK(1 + z0266 + z1147) :|: z1 >= 0, z0266 >= 0, z = 1 + (1 + z0266 + z1147) + z1 + z2, z1147 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__isNat(z0261), z1, z2) + MARK(1 + z0261) :|: z = 1 + (1 + z0261) + z1 + z2, z1 >= 0, z0261 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__U42(mark(z0265), z1146, z256), z1, z2) + MARK(1 + z0265 + z1146 + z256) :|: z1 >= 0, z = 1 + (1 + z0265 + z1146 + z256) + z1 + z2, z256 >= 0, z1146 >= 0, z0265 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__U41(mark(z0264), z1145, z255), z1, z2) + MARK(1 + z0264 + z1145 + z255) :|: z1 >= 0, z1145 >= 0, z = 1 + (1 + z0264 + z1145 + z255) + z1 + z2, z0264 >= 0, z2 >= 0, z255 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__U31(mark(z0263), z1144), z1, z2) + MARK(1 + z0263 + z1144) :|: z0263 >= 0, z1 >= 0, z = 1 + (1 + z0263 + z1144) + z1 + z2, z1144 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__U21(mark(z0262)), z1, z2) + MARK(1 + z0262) :|: z = 1 + (1 + z0262) + z1 + z2, z0262 >= 0, z1 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__U12(mark(z0260)), z1, z2) + MARK(1 + z0260) :|: z1 >= 0, z0260 >= 0, z = 1 + (1 + z0260) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(a__U11(mark(z0259), z1143), z1, z2) + MARK(1 + z0259 + z1143) :|: z1 >= 0, z0259 >= 0, z = 1 + (1 + z0259 + z1143) + z1 + z2, z1143 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(1, z1, z2) + MARK(1) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(0, z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(0, z1, z2) + MARK(0) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(1 + mark(z0267), z1, z2) + MARK(1 + z0267) :|: z1 >= 0, z0267 >= 0, z = 1 + (1 + z0267) + z1 + z2, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(a__plus(mark(z0257), mark(z1142)), z1) + MARK(1 + z0257 + z1142) :|: z1 >= 0, z0257 >= 0, z = 1 + (1 + z0257 + z1142) + z1, z1142 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(a__isNat(z0252), z1) + MARK(1 + z0252) :|: z0252 >= 0, z1 >= 0, z = 1 + (1 + z0252) + z1
   MARK(z) -{ 1 }-> 1 + A__U31(a__U42(mark(z0256), z1141, z254), z1) + MARK(1 + z0256 + z1141 + z254) :|: z0256 >= 0, z254 >= 0, z1 >= 0, z = 1 + (1 + z0256 + z1141 + z254) + z1, z1141 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(a__U41(mark(z0255), z1140, z253), z1) + MARK(1 + z0255 + z1140 + z253) :|: z1 >= 0, z253 >= 0, z0255 >= 0, z = 1 + (1 + z0255 + z1140 + z253) + z1, z1140 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(a__U31(mark(z0254), z1139), z1) + MARK(1 + z0254 + z1139) :|: z1 >= 0, z0254 >= 0, z = 1 + (1 + z0254 + z1139) + z1, z1139 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(a__U21(mark(z0253)), z1) + MARK(1 + z0253) :|: z1 >= 0, z0253 >= 0, z = 1 + (1 + z0253) + z1
   MARK(z) -{ 1 }-> 1 + A__U31(a__U12(mark(z0251)), z1) + MARK(1 + z0251) :|: z1 >= 0, z0251 >= 0, z = 1 + (1 + z0251) + z1
   MARK(z) -{ 1 }-> 1 + A__U31(a__U11(mark(z0250), z1138), z1) + MARK(1 + z0250 + z1138) :|: z1138 >= 0, z1 >= 0, z0250 >= 0, z = 1 + (1 + z0250 + z1138) + z1
   MARK(z) -{ 1 }-> 1 + A__U31(1, z - 2) + MARK(1) :|: z - 2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U31(0, z - 1) + MARK(0) :|: z - 1 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(1 + mark(z0258), z1) + MARK(1 + z0258) :|: z = 1 + (1 + z0258) + z1, z1 >= 0, z0258 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__plus(mark(z0248), mark(z1137)), z1) + MARK(1 + z0248 + z1137) :|: z1 >= 0, z0248 >= 0, z1137 >= 0, z = 1 + (1 + z0248 + z1137) + z1
   MARK(z) -{ 1 }-> 1 + A__U11(a__isNat(z0243), z1) + MARK(1 + z0243) :|: z = 1 + (1 + z0243) + z1, z1 >= 0, z0243 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U42(mark(z0247), z1136, z252), z1) + MARK(1 + z0247 + z1136 + z252) :|: z1 >= 0, z = 1 + (1 + z0247 + z1136 + z252) + z1, z1136 >= 0, z252 >= 0, z0247 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U41(mark(z0246), z1135, z251), z1) + MARK(1 + z0246 + z1135 + z251) :|: z0246 >= 0, z1 >= 0, z1135 >= 0, z251 >= 0, z = 1 + (1 + z0246 + z1135 + z251) + z1
   MARK(z) -{ 1 }-> 1 + A__U11(a__U31(mark(z0245), z1134), z1) + MARK(1 + z0245 + z1134) :|: z1134 >= 0, z = 1 + (1 + z0245 + z1134) + z1, z1 >= 0, z0245 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U21(mark(z0244)), z1) + MARK(1 + z0244) :|: z1 >= 0, z = 1 + (1 + z0244) + z1, z0244 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(a__U12(mark(z0242)), z1) + MARK(1 + z0242) :|: z0242 >= 0, z1 >= 0, z = 1 + (1 + z0242) + z1
   MARK(z) -{ 1 }-> 1 + A__U11(a__U11(mark(z0241), z1133), z1) + MARK(1 + z0241 + z1133) :|: z = 1 + (1 + z0241 + z1133) + z1, z1 >= 0, z1133 >= 0, z0241 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(1, z - 2) + MARK(1) :|: z - 2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(0, z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U11(0, z - 1) + MARK(0) :|: z - 1 >= 0
   MARK(z) -{ 1 }-> 1 + A__U11(1 + mark(z0249), z1) + MARK(1 + z0249) :|: z0249 >= 0, z1 >= 0, z = 1 + (1 + z0249) + z1
   MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__U11(z, z') -{ 0 }-> a__U12(a__U21(a__isNat(z' - 1))) :|: z = 1, z' - 1 >= 0
   a__U11(z, z') -{ 0 }-> a__U12(a__U11(a__isNat(z0511), z1283)) :|: z' = 1 + z0511 + z1283, z = 1, z1283 >= 0, z0511 >= 0
   a__U11(z, z') -{ 0 }-> 1 :|: z = 1, z' = 0, 1 = 1
   a__U11(z, z') -{ 0 }-> 1 :|: z = 1, z' >= 0, 1 + z' = 1
   a__U11(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   a__U11(z, z') -{ 0 }-> 0 :|: z = 1, z' = 0, v0 >= 0, 1 = v0
   a__U11(z, z') -{ 0 }-> 0 :|: z = 1, z' >= 0, v0 >= 0, 1 + z' = v0
   a__U11(z, z') -{ 0 }-> 0 :|: z = 1, z' >= 0, v0 >= 0, 0 = v0
   a__U11(z, z') -{ 0 }-> 1 + z0 :|: z = 1, z' = 0, 1 = z0, z0 >= 0
   a__U11(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z' >= 0, 1 + z' = z0', z0' >= 0
   a__U11(z, z') -{ 0 }-> 1 + z0' :|: z = 1, z' >= 0, 0 = z0', z0' >= 0
   a__U11(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   a__U12(z) -{ 0 }-> 1 :|: z = 1
   a__U12(z) -{ 0 }-> 0 :|: z >= 0
   a__U12(z) -{ 0 }-> 1 + z :|: z >= 0
   a__U21(z) -{ 0 }-> 1 :|: z = 1
   a__U21(z) -{ 0 }-> 0 :|: z >= 0
   a__U21(z) -{ 0 }-> 1 + z :|: z >= 0
   a__U31(z, z') -{ 0 }-> mark(z') :|: z = 1, z' >= 0
   a__U31(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   a__U31(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   a__U41(z, z', z'') -{ 0 }-> a__U42(a__U21(a__isNat(z'' - 1)), z', 1 + (z'' - 1)) :|: z = 1, z'' - 1 >= 0, z' >= 0
   a__U41(z, z', z'') -{ 0 }-> a__U42(a__U11(a__isNat(z0513), z1284), z', 1 + z0513 + z1284) :|: z = 1, z1284 >= 0, z' >= 0, z0513 >= 0, z'' = 1 + z0513 + z1284
   a__U41(z, z', z'') -{ 0 }-> a__U42(1, z', 0) :|: z'' = 0, z = 1, z' >= 0
   a__U41(z, z', z'') -{ 0 }-> a__U42(0, z', z'') :|: z'' >= 0, z = 1, z' >= 0
   a__U41(z, z', z'') -{ 0 }-> a__U42(1 + z'', z', z'') :|: z'' >= 0, z = 1, z' >= 0
   a__U41(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   a__U41(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0
   a__U42(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   a__U42(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z''), mark(z')) :|: z'' >= 0, z = 1, z' >= 0
   a__U42(z, z', z'') -{ 0 }-> 1 + z + z' + z'' :|: z' >= 0, z >= 0, z'' >= 0
   a__isNat(z) -{ 0 }-> a__U21(a__U21(a__isNat(z - 2))) :|: z - 2 >= 0
   a__isNat(z) -{ 0 }-> a__U21(a__U11(a__isNat(z0634), z1351)) :|: z0634 >= 0, z = 1 + (1 + z0634 + z1351), z1351 >= 0
   a__isNat(z) -{ 0 }-> a__U11(a__U21(a__isNat(z0633)), z1) :|: z1 >= 0, z0633 >= 0, z = 1 + (1 + z0633) + z1
   a__isNat(z) -{ 0 }-> a__U11(a__U11(a__isNat(z0632), z1350), z1) :|: z1 >= 0, z0632 >= 0, z1350 >= 0, z = 1 + (1 + z0632 + z1350) + z1
   a__isNat(z) -{ 0 }-> a__U11(1, z - 1) :|: z - 1 >= 0
   a__isNat(z) -{ 0 }-> a__U11(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNat(z) -{ 0 }-> a__U11(1 + z0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNat(z) -{ 0 }-> 1 :|: z = 0
   a__isNat(z) -{ 0 }-> 1 :|: z = 1 + 0, 1 = 1
   a__isNat(z) -{ 0 }-> 1 :|: z - 1 >= 0, 1 + (z - 1) = 1
   a__isNat(z) -{ 0 }-> 0 :|: z >= 0
   a__isNat(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 1 = v0
   a__isNat(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 1 + (z - 1) = v0
   a__isNat(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   a__isNat(z) -{ 0 }-> 1 + z :|: z >= 0
   a__isNat(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 1 = z0, z0 >= 0
   a__isNat(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 1 + (z - 1) = z0', z0' >= 0
   a__isNat(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   a__plus(z, z') -{ 0 }-> a__U41(a__U21(a__isNat(z' - 2)), 1 + (z' - 2), z) :|: z' - 2 >= 0, z >= 0
   a__plus(z, z') -{ 0 }-> a__U41(a__U11(a__isNat(z0638), z1353), 1 + z0638 + z1353, z) :|: z1353 >= 0, z' = 1 + (1 + z0638 + z1353), z >= 0, z0638 >= 0
   a__plus(z, z') -{ 0 }-> a__U41(1, 0, z) :|: z' = 1 + 0, z >= 0
   a__plus(z, z') -{ 0 }-> a__U41(0, z' - 1, z) :|: z' - 1 >= 0, z >= 0
   a__plus(z, z') -{ 0 }-> a__U41(1 + (z' - 1), z' - 1, z) :|: z' - 1 >= 0, z >= 0
   a__plus(z, z') -{ 0 }-> a__U31(a__U21(a__isNat(z - 1)), 1 + (z - 1)) :|: z - 1 >= 0, z' = 0
   a__plus(z, z') -{ 0 }-> a__U31(a__U11(a__isNat(z0636), z1352), 1 + z0636 + z1352) :|: z = 1 + z0636 + z1352, z1352 >= 0, z0636 >= 0, z' = 0
   a__plus(z, z') -{ 0 }-> a__U31(1, 0) :|: z = 0, z' = 0
   a__plus(z, z') -{ 0 }-> a__U31(0, z) :|: z >= 0, z' = 0
   a__plus(z, z') -{ 0 }-> a__U31(1 + z, z) :|: z >= 0, z' = 0
   a__plus(z, z') -{ 0 }-> 0 :|: z >= 0, z' >= 0
   a__plus(z, z') -{ 0 }-> 1 + z + z' :|: z' >= 0, z >= 0
   mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__isNat(z - 1) :|: z - 1 >= 0
   mark(z) -{ 0 }-> a__U42(a__plus(mark(z0692), mark(z1383)), z1, z2) :|: z1 >= 0, z1383 >= 0, z = 1 + (1 + z0692 + z1383) + z1 + z2, z0692 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__isNat(z0687), z1, z2) :|: z0687 >= 0, z = 1 + (1 + z0687) + z1 + z2, z1 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__U42(mark(z0691), z1382, z2148), z1, z2) :|: z1 >= 0, z2148 >= 0, z1382 >= 0, z = 1 + (1 + z0691 + z1382 + z2148) + z1 + z2, z0691 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__U41(mark(z0690), z1381, z2147), z1, z2) :|: z = 1 + (1 + z0690 + z1381 + z2147) + z1 + z2, z1 >= 0, z1381 >= 0, z2147 >= 0, z0690 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__U31(mark(z0689), z1380), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0689 + z1380) + z1 + z2, z1380 >= 0, z0689 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__U21(mark(z0688)), z1, z2) :|: z = 1 + (1 + z0688) + z1 + z2, z1 >= 0, z0688 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__U12(mark(z0686)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0686) + z1 + z2, z0686 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(a__U11(mark(z0685), z1379), z1, z2) :|: z1 >= 0, z1379 >= 0, z = 1 + (1 + z0685 + z1379) + z1 + z2, z0685 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U42(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U42(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U42(1 + mark(z0693), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0693) + z1 + z2, z0693 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U41(a__plus(mark(z0683), mark(z1378)), z1, z2) :|: z0683 >= 0, z1 >= 0, z1378 >= 0, z = 1 + (1 + z0683 + z1378) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U41(a__isNat(z0678), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0678) + z1 + z2, z0678 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U41(a__U42(mark(z0682), z1377, z2146), z1, z2) :|: z2146 >= 0, z1 >= 0, z0682 >= 0, z = 1 + (1 + z0682 + z1377 + z2146) + z1 + z2, z1377 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U41(a__U41(mark(z0681), z1376, z2145), z1, z2) :|: z1 >= 0, z0681 >= 0, z = 1 + (1 + z0681 + z1376 + z2145) + z1 + z2, z2145 >= 0, z2 >= 0, z1376 >= 0
   mark(z) -{ 0 }-> a__U41(a__U31(mark(z0680), z1375), z1, z2) :|: z1 >= 0, z0680 >= 0, z = 1 + (1 + z0680 + z1375) + z1 + z2, z1375 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U41(a__U21(mark(z0679)), z1, z2) :|: z1 >= 0, z = 1 + (1 + z0679) + z1 + z2, z0679 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U41(a__U12(mark(z0677)), z1, z2) :|: z1 >= 0, z0677 >= 0, z2 >= 0, z = 1 + (1 + z0677) + z1 + z2
   mark(z) -{ 0 }-> a__U41(a__U11(mark(z0676), z1374), z1, z2) :|: z0676 >= 0, z1 >= 0, z1374 >= 0, z = 1 + (1 + z0676 + z1374) + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U41(1, z1, z2) :|: z1 >= 0, z = 1 + 1 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U41(0, z1, z2) :|: z1 >= 0, z = 1 + 0 + z1 + z2, z2 >= 0
   mark(z) -{ 0 }-> a__U41(0, z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U41(1 + mark(z0684), z1, z2) :|: z1 >= 0, z0684 >= 0, z2 >= 0, z = 1 + (1 + z0684) + z1 + z2
   mark(z) -{ 0 }-> a__U31(a__plus(mark(z0674), mark(z1373)), z1) :|: z1 >= 0, z1373 >= 0, z0674 >= 0, z = 1 + (1 + z0674 + z1373) + z1
   mark(z) -{ 0 }-> a__U31(a__isNat(z0669), z1) :|: z1 >= 0, z = 1 + (1 + z0669) + z1, z0669 >= 0
   mark(z) -{ 0 }-> a__U31(a__U42(mark(z0673), z1372, z2144), z1) :|: z1 >= 0, z0673 >= 0, z1372 >= 0, z2144 >= 0, z = 1 + (1 + z0673 + z1372 + z2144) + z1
   mark(z) -{ 0 }-> a__U31(a__U41(mark(z0672), z1371, z2143), z1) :|: z0672 >= 0, z1 >= 0, z1371 >= 0, z = 1 + (1 + z0672 + z1371 + z2143) + z1, z2143 >= 0
   mark(z) -{ 0 }-> a__U31(a__U31(mark(z0671), z1370), z1) :|: z1 >= 0, z1370 >= 0, z = 1 + (1 + z0671 + z1370) + z1, z0671 >= 0
   mark(z) -{ 0 }-> a__U31(a__U21(mark(z0670)), z1) :|: z1 >= 0, z = 1 + (1 + z0670) + z1, z0670 >= 0
   mark(z) -{ 0 }-> a__U31(a__U12(mark(z0668)), z1) :|: z1 >= 0, z = 1 + (1 + z0668) + z1, z0668 >= 0
   mark(z) -{ 0 }-> a__U31(a__U11(mark(z0667), z1369), z1) :|: z1 >= 0, z = 1 + (1 + z0667 + z1369) + z1, z1369 >= 0, z0667 >= 0
   mark(z) -{ 0 }-> a__U31(1, z - 2) :|: z - 2 >= 0
   mark(z) -{ 0 }-> a__U31(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U31(0, z - 1) :|: z - 1 >= 0
   mark(z) -{ 0 }-> a__U31(1 + mark(z0675), z1) :|: z1 >= 0, z = 1 + (1 + z0675) + z1, z0675 >= 0
   mark(z) -{ 0 }-> a__U21(a__plus(mark(z0665), mark(z1368))) :|: z1368 >= 0, z0665 >= 0, z = 1 + (1 + z0665 + z1368)
   mark(z) -{ 0 }-> a__U21(a__isNat(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 0 }-> a__U21(a__U42(mark(z0664), z1367, z2142)) :|: z = 1 + (1 + z0664 + z1367 + z2142), z1367 >= 0, z2142 >= 0, z0664 >= 0
   mark(z) -{ 0 }-> a__U21(a__U41(mark(z0663), z1366, z2141)) :|: z = 1 + (1 + z0663 + z1366 + z2141), z0663 >= 0, z2141 >= 0, z1366 >= 0
   mark(z) -{ 0 }-> a__U21(a__U31(mark(z0662), z1365)) :|: z0662 >= 0, z = 1 + (1 + z0662 + z1365), z1365 >= 0
   mark(z) -{ 0 }-> a__U21(a__U21(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 0 }-> a__U21(a__U12(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 0 }-> a__U21(a__U11(mark(z0658), z1364)) :|: z1364 >= 0, z = 1 + (1 + z0658 + z1364), z0658 >= 0
   mark(z) -{ 0 }-> a__U21(1 + mark(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 0 }-> a__U12(a__plus(mark(z0656), mark(z1363))) :|: z1363 >= 0, z0656 >= 0, z = 1 + (1 + z0656 + z1363)
   mark(z) -{ 0 }-> a__U12(a__isNat(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 0 }-> a__U12(a__U42(mark(z0655), z1362, z2140)) :|: z0655 >= 0, z2140 >= 0, z1362 >= 0, z = 1 + (1 + z0655 + z1362 + z2140)
   mark(z) -{ 0 }-> a__U12(a__U41(mark(z0654), z1361, z2139)) :|: z = 1 + (1 + z0654 + z1361 + z2139), z2139 >= 0, z0654 >= 0, z1361 >= 0
   mark(z) -{ 0 }-> a__U12(a__U31(mark(z0653), z1360)) :|: z1360 >= 0, z0653 >= 0, z = 1 + (1 + z0653 + z1360)
   mark(z) -{ 0 }-> a__U12(a__U21(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 0 }-> a__U12(a__U12(mark(z - 2))) :|: z - 2 >= 0
   mark(z) -{ 0 }-> a__U12(a__U11(mark(z0649), z1359)) :|: z0649 >= 0, z = 1 + (1 + z0649 + z1359), z1359 >= 0
   mark(z) -{ 0 }-> a__U12(1 + mark(z - 2)) :|: z - 2 >= 0
   mark(z) -{ 0 }-> a__U11(a__plus(mark(z0647), mark(z1358)), z1) :|: z1 >= 0, z0647 >= 0, z = 1 + (1 + z0647 + z1358) + z1, z1358 >= 0
   mark(z) -{ 0 }-> a__U11(a__isNat(z0642), z1) :|: z = 1 + (1 + z0642) + z1, z1 >= 0, z0642 >= 0
   mark(z) -{ 0 }-> a__U11(a__U42(mark(z0646), z1357, z2138), z1) :|: z1357 >= 0, z1 >= 0, z = 1 + (1 + z0646 + z1357 + z2138) + z1, z2138 >= 0, z0646 >= 0
   mark(z) -{ 0 }-> a__U11(a__U41(mark(z0645), z1356, z2137), z1) :|: z = 1 + (1 + z0645 + z1356 + z2137) + z1, z0645 >= 0, z1 >= 0, z2137 >= 0, z1356 >= 0
   mark(z) -{ 0 }-> a__U11(a__U31(mark(z0644), z1355), z1) :|: z1 >= 0, z0644 >= 0, z1355 >= 0, z = 1 + (1 + z0644 + z1355) + z1
   mark(z) -{ 0 }-> a__U11(a__U21(mark(z0643)), z1) :|: z1 >= 0, z0643 >= 0, z = 1 + (1 + z0643) + z1
   mark(z) -{ 0 }-> a__U11(a__U12(mark(z0641)), z1) :|: z0641 >= 0, z1 >= 0, z = 1 + (1 + z0641) + z1
   mark(z) -{ 0 }-> a__U11(a__U11(mark(z0640), z1354), z1) :|: z1 >= 0, z1354 >= 0, z = 1 + (1 + z0640 + z1354) + z1, z0640 >= 0
   mark(z) -{ 0 }-> a__U11(1, z - 2) :|: z - 2 >= 0
   mark(z) -{ 0 }-> a__U11(0, z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U11(0, z - 1) :|: z - 1 >= 0
   mark(z) -{ 0 }-> a__U11(1 + mark(z0648), z1) :|: z1 >= 0, z = 1 + (1 + z0648) + z1, z0648 >= 0
   mark(z) -{ 0 }-> 1 :|: z = 1
   mark(z) -{ 0 }-> 1 :|: z = 1 + 1, 1 = 1
   mark(z) -{ 0 }-> 0 :|: z = 0
   mark(z) -{ 0 }-> 0 :|: z >= 0
   mark(z) -{ 0 }-> 0 :|: z = 1 + 1, v0 >= 0, 1 = v0
   mark(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   mark(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 1, 1 = z0, z0 >= 0
   mark(z) -{ 0 }-> 1 + z0 :|: z = 1 + 0, 0 = z0, z0 >= 0
   mark(z) -{ 0 }-> 1 + z0' :|: z - 1 >= 0, 0 = z0', z0' >= 0
   mark(z) -{ 0 }-> 1 + mark(z - 1) :|: z - 1 >= 0


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

(67) 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__U11(v0, v1) -> null_a__U11 [0]
   a__U12(v0) -> null_a__U12 [0]
   a__U21(v0) -> null_a__U21 [0]
   a__U31(v0, v1) -> null_a__U31 [0]
   a__U41(v0, v1, v2) -> null_a__U41 [0]
   a__U42(v0, v1, v2) -> null_a__U42 [0]
   a__isNat(v0) -> null_a__isNat [0]
   a__plus(v0, v1) -> null_a__plus [0]
   mark(v0) -> null_mark [0]
   A__U31(v0, v1) -> null_A__U31 [0]
   A__U41(v0, v1, v2) -> null_A__U41 [0]
   A__U42(v0, v1, v2) -> null_A__U42 [0]
   A__ISNAT(v0) -> null_A__ISNAT [0]
   A__PLUS(v0, v1) -> null_A__PLUS [0]
   MARK(v0) -> null_MARK [0]
   A__U11(v0, v1) -> null_A__U11 [0]

And the following fresh constants:    null_a__U11, null_a__U12, null_a__U21, null_a__U31, null_a__U41, null_a__U42, null_a__isNat, null_a__plus, null_mark, null_A__U31, null_A__U41, null_A__U42, null_A__ISNAT, null_A__PLUS, null_MARK, null_A__U11

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

(68)
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__U31(tt, z0) -> c6(MARK(z0)) [1]
   A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1)) [1]
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1]
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1]
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) [1]
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) [1]
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) [1]
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) [1]
   MARK(isNat(z0)) -> c22(A__ISNAT(z0)) [1]
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) [1]
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1]
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1]
   MARK(s(z0)) -> c30(MARK(z0)) [1]
   A__U11(tt, z0) -> c(A__ISNAT(z0)) [1]
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0)) [1]
   MARK(U12(z0)) -> c21(MARK(z0)) [1]
   MARK(U21(z0)) -> c23(MARK(z0)) [1]
   a__U11(tt, z0) -> a__U12(a__isNat(z0)) [0]
   a__U11(z0, z1) -> U11(z0, z1) [0]
   a__U12(tt) -> tt [0]
   a__U12(z0) -> U12(z0) [0]
   a__U21(tt) -> tt [0]
   a__U21(z0) -> U21(z0) [0]
   a__U31(tt, z0) -> mark(z0) [0]
   a__U31(z0, z1) -> U31(z0, z1) [0]
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1) [0]
   a__U41(z0, z1, z2) -> U41(z0, z1, z2) [0]
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0]
   a__U42(z0, z1, z2) -> U42(z0, z1, z2) [0]
   a__isNat(0) -> tt [0]
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) [0]
   a__isNat(s(z0)) -> a__U21(a__isNat(z0)) [0]
   a__isNat(z0) -> isNat(z0) [0]
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0) [0]
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0) [0]
   a__plus(z0, z1) -> plus(z0, z1) [0]
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0]
   mark(U12(z0)) -> a__U12(mark(z0)) [0]
   mark(isNat(z0)) -> a__isNat(z0) [0]
   mark(U21(z0)) -> a__U21(mark(z0)) [0]
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0]
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2) [0]
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2) [0]
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0]
   mark(tt) -> tt [0]
   mark(s(z0)) -> s(mark(z0)) [0]
   mark(0) -> 0 [0]
   a__U11(v0, v1) -> null_a__U11 [0]
   a__U12(v0) -> null_a__U12 [0]
   a__U21(v0) -> null_a__U21 [0]
   a__U31(v0, v1) -> null_a__U31 [0]
   a__U41(v0, v1, v2) -> null_a__U41 [0]
   a__U42(v0, v1, v2) -> null_a__U42 [0]
   a__isNat(v0) -> null_a__isNat [0]
   a__plus(v0, v1) -> null_a__plus [0]
   mark(v0) -> null_mark [0]
   A__U31(v0, v1) -> null_A__U31 [0]
   A__U41(v0, v1, v2) -> null_A__U41 [0]
   A__U42(v0, v1, v2) -> null_A__U42 [0]
   A__ISNAT(v0) -> null_A__ISNAT [0]
   A__PLUS(v0, v1) -> null_A__PLUS [0]
   MARK(v0) -> null_MARK [0]
   A__U11(v0, v1) -> null_A__U11 [0]

The TRS has the following type information:
A__U31 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c6:null_A__U31
tt :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c6 :: c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK -> c6:null_A__U31
MARK :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK
A__U41 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c8:null_A__U41
c8 :: c10:c11:null_A__U42 -> c14:c15:null_A__ISNAT -> c8:null_A__U41
A__U42 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c10:c11:null_A__U42
a__isNat :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
A__ISNAT :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c14:c15:null_A__ISNAT
c10 :: c17:c18:null_A__PLUS -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK -> c10:c11:null_A__U42
A__PLUS :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c17:c18:null_A__PLUS
mark :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c11 :: c17:c18:null_A__PLUS -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK -> c10:c11:null_A__U42
plus :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c14 :: c:null_A__U11 -> c14:c15:null_A__ISNAT -> c14:c15:null_A__ISNAT
A__U11 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> c:null_A__U11
0 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c17 :: c6:null_A__U31 -> c14:c15:null_A__ISNAT -> c17:c18:null_A__PLUS
s :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c18 :: c8:null_A__U41 -> c14:c15:null_A__ISNAT -> c17:c18:null_A__PLUS
U11 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c20 :: c:null_A__U11 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK
isNat :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c22 :: c14:c15:null_A__ISNAT -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK
U31 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c24 :: c6:null_A__U31 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK
U41 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c25 :: c8:null_A__U41 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK
U42 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c26 :: c10:c11:null_A__U42 -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK
c27 :: c17:c18:null_A__PLUS -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK
c28 :: c17:c18:null_A__PLUS -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK
c30 :: c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK
c :: c14:c15:null_A__ISNAT -> c:null_A__U11
c15 :: c14:c15:null_A__ISNAT -> c14:c15:null_A__ISNAT
U12 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c21 :: c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK
U21 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
c23 :: c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK -> c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK
a__U11 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
a__U12 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
a__U21 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
a__U31 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
a__U41 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
a__U42 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
a__plus :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark -> tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__U11 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__U12 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__U21 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__U31 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__U41 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__U42 :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__isNat :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_a__plus :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_mark :: tt:plus:0:s:U11:isNat:U31:U41:U42:U12:U21:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U41:null_a__U42:null_a__isNat:null_a__plus:null_mark
null_A__U31 :: c6:null_A__U31
null_A__U41 :: c8:null_A__U41
null_A__U42 :: c10:c11:null_A__U42
null_A__ISNAT :: c14:c15:null_A__ISNAT
null_A__PLUS :: c17:c18:null_A__PLUS
null_MARK :: c20:c22:c24:c25:c26:c27:c28:c30:c21:c23:null_MARK
null_A__U11 :: c:null_A__U11

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

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

   tt => 1
   0 => 0
   null_a__U11 => 0
   null_a__U12 => 0
   null_a__U21 => 0
   null_a__U31 => 0
   null_a__U41 => 0
   null_a__U42 => 0
   null_a__isNat => 0
   null_a__plus => 0
   null_mark => 0
   null_A__U31 => 0
   null_A__U41 => 0
   null_A__U42 => 0
   null_A__ISNAT => 0
   null_A__PLUS => 0
   null_MARK => 0
   null_A__U11 => 0

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

(70)
Obligation:
Complexity RNTS consisting of the following rules:

   A__ISNAT(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   A__ISNAT(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0
   A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__isNat(z0), z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   A__PLUS(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   A__PLUS(z, z') -{ 1 }-> 1 + A__U41(a__isNat(z1), z1, z0) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   A__PLUS(z, z') -{ 1 }-> 1 + A__U31(a__isNat(z0), z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0
   A__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   A__U11(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1, z0 >= 0, z' = z0
   A__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   A__U31(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 1, z0 >= 0, z' = z0
   A__U41(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   A__U41(z, z', z'') -{ 1 }-> 1 + A__U42(a__isNat(z1), z0, z1) + A__ISNAT(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U42(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   A__U42(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   A__U42(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0
   MARK(z) -{ 1 }-> 1 + A__U42(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U41(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   MARK(z) -{ 1 }-> 1 + A__U31(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__U11(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__U11(z, z') -{ 0 }-> a__U12(a__isNat(z0)) :|: z = 1, z0 >= 0, z' = z0
   a__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U11(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U12(z) -{ 0 }-> 1 :|: z = 1
   a__U12(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U12(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U21(z) -{ 0 }-> 1 :|: z = 1
   a__U21(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__U21(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__U31(z, z') -{ 0 }-> mark(z0) :|: z = 1, z0 >= 0, z' = z0
   a__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__U31(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   a__U41(z, z', z'') -{ 0 }-> a__U42(a__isNat(z1), z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__U41(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U41(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__U42(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   a__U42(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z1), mark(z0)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1
   a__U42(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0
   a__isNat(z) -{ 0 }-> a__U21(a__isNat(z0)) :|: z = 1 + z0, z0 >= 0
   a__isNat(z) -{ 0 }-> a__U11(a__isNat(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   a__isNat(z) -{ 0 }-> 1 :|: z = 0
   a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0
   a__plus(z, z') -{ 0 }-> a__U41(a__isNat(z1), z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1
   a__plus(z, z') -{ 0 }-> a__U31(a__isNat(z0), z0) :|: z = z0, z0 >= 0, z' = 0
   a__plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1
   a__plus(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0
   mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U42(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U41(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0
   mark(z) -{ 0 }-> a__U31(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   mark(z) -{ 0 }-> a__U21(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U12(mark(z0)) :|: z = 1 + z0, z0 >= 0
   mark(z) -{ 0 }-> a__U11(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1
   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

Only complete derivations are relevant for the runtime complexity.

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

(71) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, z0, z1) -> c8(A__U42(a__isNat(z1), z0, z1), A__ISNAT(z1)) by 
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0), A__ISNAT(0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, z0) -> c8(A__U42(isNat(z0), x0, z0), A__ISNAT(z0))

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

(72)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0), A__ISNAT(0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, z0) -> c8(A__U42(isNat(z0), x0, z0), A__ISNAT(z0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0), A__ISNAT(0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, z0) -> c8(A__U42(isNat(z0), x0, z0), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__U42_3, A__ISNAT_1, A__PLUS_2, MARK_1, A__U11_2, A__U41_3

Compound Symbols:   c6_1, c10_2, c11_2, c14_2, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2


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

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

(74)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__U42_3, A__ISNAT_1, A__PLUS_2, MARK_1, A__U11_2, A__U41_3

Compound Symbols:   c6_1, c10_2, c11_2, c14_2, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1


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

(75) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, z0, z1) -> c10(A__PLUS(mark(z1), mark(z0)), MARK(z1)) by 
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, tt, x1) -> c10(A__PLUS(mark(x1), tt), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)), MARK(tt))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)), MARK(0))

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

(76)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, tt, x1) -> c10(A__PLUS(mark(x1), tt), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)), MARK(tt))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)), MARK(0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, tt, x1) -> c10(A__PLUS(mark(x1), tt), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)), MARK(tt))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__U42_3, A__ISNAT_1, A__PLUS_2, MARK_1, A__U11_2, A__U41_3

Compound Symbols:   c6_1, c11_2, c14_2, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2


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

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

(78)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__U42_3, A__ISNAT_1, A__PLUS_2, MARK_1, A__U11_2, A__U41_3

Compound Symbols:   c6_1, c11_2, c14_2, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1


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

(79) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, z0, z1) -> c11(A__PLUS(mark(z1), mark(z0)), MARK(z0)) by 
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, tt, x1) -> c11(A__PLUS(mark(x1), tt), MARK(tt))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0), MARK(0))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))

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

(80)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, tt, x1) -> c11(A__PLUS(mark(x1), tt), MARK(tt))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0), MARK(0))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, tt, x1) -> c11(A__PLUS(mark(x1), tt), MARK(tt))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0), MARK(0))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__ISNAT_1, A__PLUS_2, MARK_1, A__U11_2, A__U41_3, A__U42_3

Compound Symbols:   c6_1, c14_2, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2


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

(81) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U42(tt, tt, x1) -> c11(A__PLUS(mark(x1), tt), MARK(tt))

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

(82)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0), MARK(0))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0), MARK(0))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__ISNAT_1, A__PLUS_2, MARK_1, A__U11_2, A__U41_3, A__U42_3

Compound Symbols:   c6_1, c14_2, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2


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

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

(84)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__ISNAT_1, A__PLUS_2, MARK_1, A__U11_2, A__U41_3, A__U42_3

Compound Symbols:   c6_1, c14_2, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1


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

(85) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__ISNAT(plus(z0, z1)) -> c14(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) by 
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1), A__ISNAT(0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c14(A__U11(isNat(z0), x1), A__ISNAT(z0))

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

(86)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1), A__ISNAT(0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c14(A__U11(isNat(z0), x1), A__ISNAT(z0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1), A__ISNAT(0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(z0, x1)) -> c14(A__U11(isNat(z0), x1), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__PLUS_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3

Compound Symbols:   c6_1, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2


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

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

(88)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__PLUS_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3

Compound Symbols:   c6_1, c17_2, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1


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

(89) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__PLUS(z0, 0) -> c17(A__U31(a__isNat(z0), z0), A__ISNAT(z0)) by 
   A__PLUS(0, 0) -> c17(A__U31(tt, 0), A__ISNAT(0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c17(A__U31(isNat(z0), z0), A__ISNAT(z0))

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

(90)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0), A__ISNAT(0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c17(A__U31(isNat(z0), z0), A__ISNAT(z0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0), A__ISNAT(0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(z0, 0) -> c17(A__U31(isNat(z0), z0), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__PLUS_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3

Compound Symbols:   c6_1, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2


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

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

(92)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, A__PLUS_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3

Compound Symbols:   c6_1, c18_2, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1


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

(93) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__PLUS(z0, s(z1)) -> c18(A__U41(a__isNat(z1), z1, z0), A__ISNAT(z1)) by 
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0), A__ISNAT(0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c18(A__U41(isNat(z0), z0, x0), A__ISNAT(z0))

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

(94)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0), A__ISNAT(0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c18(A__U41(isNat(z0), z0, x0), A__ISNAT(z0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0), A__ISNAT(0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(z0)) -> c18(A__U41(isNat(z0), z0, x0), A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2


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

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

(96)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c20_2, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1


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(97) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U11(z0, z1)) -> c20(A__U11(mark(z0), z1), MARK(z0)) by 
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNat(z0), x1)) -> c20(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1), MARK(tt))
   MARK(U11(s(z0), x1)) -> c20(A__U11(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U11(0, x1)) -> c20(A__U11(0, x1), MARK(0))

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

(98)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNat(z0), x1)) -> c20(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1), MARK(tt))
   MARK(U11(s(z0), x1)) -> c20(A__U11(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U11(0, x1)) -> c20(A__U11(0, x1), MARK(0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNat(z0), x1)) -> c20(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1), MARK(tt))
   MARK(U11(s(z0), x1)) -> c20(A__U11(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U11(0, x1)) -> c20(A__U11(0, x1), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2


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

(99) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(U11(0, x1)) -> c20(A__U11(0, x1), MARK(0))

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

(100)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNat(z0), x1)) -> c20(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1), MARK(tt))
   MARK(U11(s(z0), x1)) -> c20(A__U11(s(mark(z0)), x1), MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNat(z0), x1)) -> c20(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1), MARK(tt))
   MARK(U11(s(z0), x1)) -> c20(A__U11(s(mark(z0)), x1), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2


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

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

(102)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNat(z0), x1)) -> c20(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(isNat(z0), x1)) -> c20(A__U11(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1


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

(103) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID))
Split RHS of tuples not part of any SCC
----------------------------------------

(104)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c24_2, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1


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

(105) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U31(z0, z1)) -> c24(A__U31(mark(z0), z1), MARK(z0)) by 
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1), MARK(tt))
   MARK(U31(s(z0), x1)) -> c24(A__U31(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U31(0, x1)) -> c24(A__U31(0, x1), MARK(0))

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

(106)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1), MARK(tt))
   MARK(U31(s(z0), x1)) -> c24(A__U31(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U31(0, x1)) -> c24(A__U31(0, x1), MARK(0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1), MARK(tt))
   MARK(U31(s(z0), x1)) -> c24(A__U31(s(mark(z0)), x1), MARK(s(z0)))
   MARK(U31(0, x1)) -> c24(A__U31(0, x1), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2


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

(107) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(U31(0, x1)) -> c24(A__U31(0, x1), MARK(0))

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

(108)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1), MARK(tt))
   MARK(U31(s(z0), x1)) -> c24(A__U31(s(mark(z0)), x1), MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1), MARK(tt))
   MARK(U31(s(z0), x1)) -> c24(A__U31(s(mark(z0)), x1), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2


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

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

(110)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c25_2, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1


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

(111) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U41(z0, z1, z2)) -> c25(A__U41(mark(z0), z1, z2), MARK(z0)) by 
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2), MARK(tt))
   MARK(U41(s(z0), x1, x2)) -> c25(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U41(0, x1, x2)) -> c25(A__U41(0, x1, x2), MARK(0))

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

(112)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2), MARK(tt))
   MARK(U41(s(z0), x1, x2)) -> c25(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U41(0, x1, x2)) -> c25(A__U41(0, x1, x2), MARK(0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2), MARK(tt))
   MARK(U41(s(z0), x1, x2)) -> c25(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U41(0, x1, x2)) -> c25(A__U41(0, x1, x2), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2


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

(113) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(U41(0, x1, x2)) -> c25(A__U41(0, x1, x2), MARK(0))

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

(114)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2), MARK(tt))
   MARK(U41(s(z0), x1, x2)) -> c25(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2), MARK(tt))
   MARK(U41(s(z0), x1, x2)) -> c25(A__U41(s(mark(z0)), x1, x2), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2


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

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

(116)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c26_2, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1


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

(117) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(U42(z0, z1, z2)) -> c26(A__U42(mark(z0), z1, z2), MARK(z0)) by 
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2), MARK(tt))
   MARK(U42(s(z0), x1, x2)) -> c26(A__U42(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U42(0, x1, x2)) -> c26(A__U42(0, x1, x2), MARK(0))

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

(118)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2), MARK(tt))
   MARK(U42(s(z0), x1, x2)) -> c26(A__U42(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U42(0, x1, x2)) -> c26(A__U42(0, x1, x2), MARK(0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2), MARK(tt))
   MARK(U42(s(z0), x1, x2)) -> c26(A__U42(s(mark(z0)), x1, x2), MARK(s(z0)))
   MARK(U42(0, x1, x2)) -> c26(A__U42(0, x1, x2), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2


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

(119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(U42(0, x1, x2)) -> c26(A__U42(0, x1, x2), MARK(0))

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

(120)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2), MARK(tt))
   MARK(U42(s(z0), x1, x2)) -> c26(A__U42(s(mark(z0)), x1, x2), MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2), MARK(tt))
   MARK(U42(s(z0), x1, x2)) -> c26(A__U42(s(mark(z0)), x1, x2), MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2


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

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

(122)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c27_2, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1


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

(123) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(plus(z0, z1)) -> c27(A__PLUS(mark(z0), mark(z1)), MARK(z0)) by 
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, tt)) -> c27(A__PLUS(mark(x0), tt), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(tt))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(0))

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

(124)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, tt)) -> c27(A__PLUS(mark(x0), tt), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(tt))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, tt)) -> c27(A__PLUS(mark(x0), tt), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)), MARK(tt))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2


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

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

(126)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c28_2, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1


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

(127) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace MARK(plus(z0, z1)) -> c28(A__PLUS(mark(z0), mark(z1)), MARK(z1)) by 
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, tt)) -> c28(A__PLUS(mark(x0), tt), MARK(tt))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))

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

(128)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, tt)) -> c28(A__PLUS(mark(x0), tt), MARK(tt))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, tt)) -> c28(A__PLUS(mark(x0), tt), MARK(tt))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2


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

(129) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   MARK(plus(x0, tt)) -> c28(A__PLUS(mark(x0), tt), MARK(tt))

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

(130)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0), MARK(0))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2


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

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

(132)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1


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

(133) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, x0, plus(z0, z1)) -> c8(A__U42(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) by 
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__U42(U11(a__isNat(x1), z1), x0, plus(x1, z1)), A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))

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

(134)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__U42(U11(a__isNat(x1), z1), x0, plus(x1, z1)), A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__U42(U11(a__isNat(x1), z1), x0, plus(x1, z1)), A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1


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

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

(136)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_2, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1


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

(137) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) by 
   A__U41(tt, x0, s(x1)) -> c8(A__U42(U21(a__isNat(x1)), x0, s(x1)), A__ISNAT(s(x1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))

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

(138)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(x1)) -> c8(A__U42(U21(a__isNat(x1)), x0, s(x1)), A__ISNAT(s(x1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(x1)) -> c8(A__U42(U21(a__isNat(x1)), x0, s(x1)), A__ISNAT(s(x1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(140)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(141) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, U11(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) by 
   A__U42(tt, U11(x0, z1), x2) -> c10(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(x2))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(tt))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)), MARK(0))

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

(142)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(x0, z1), x2) -> c10(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(x2))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(tt))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)), MARK(0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(x0, z1), x2) -> c10(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(x2))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(tt))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(144)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(145) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, U12(z0), x1) -> c10(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) by 
   A__U42(tt, U12(x0), x1) -> c10(A__PLUS(mark(x1), U12(mark(x0))), MARK(x1))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))), MARK(tt))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))), MARK(0))

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

(146)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(x0), x1) -> c10(A__PLUS(mark(x1), U12(mark(x0))), MARK(x1))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))), MARK(tt))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))), MARK(0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(x0), x1) -> c10(A__PLUS(mark(x1), U12(mark(x0))), MARK(x1))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))), MARK(tt))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(148)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
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   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(149) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) by 
   A__U42(tt, isNat(0), x1) -> c10(A__PLUS(mark(x1), tt), MARK(x1))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), isNat(z0)), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)), MARK(tt))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)), MARK(0))

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

(150)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(0), x1) -> c10(A__PLUS(mark(x1), tt), MARK(x1))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), isNat(z0)), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)), MARK(tt))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)), MARK(0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(0), x1) -> c10(A__PLUS(mark(x1), tt), MARK(x1))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(A__PLUS(mark(x1), isNat(z0)), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)), MARK(tt))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(152)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
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   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(153) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, U21(z0), x1) -> c10(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) by 
   A__U42(tt, U21(x0), x1) -> c10(A__PLUS(mark(x1), U21(mark(x0))), MARK(x1))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))), MARK(tt))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))), MARK(0))

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

(154)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
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   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(x0), x1) -> c10(A__PLUS(mark(x1), U21(mark(x0))), MARK(x1))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))), MARK(tt))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))), MARK(0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(x0), x1) -> c10(A__PLUS(mark(x1), U21(mark(x0))), MARK(x1))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))), MARK(tt))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(156)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
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   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(157) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, U31(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) by 
   A__U42(tt, U31(x0, z1), x2) -> c10(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(x2))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(tt))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)), MARK(0))

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

(158)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
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   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(tt))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)), MARK(0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
   A__U42(tt, U31(x0, z1), x2) -> c10(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(x2))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(tt))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(160)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
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   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(161) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, U41(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(x1)) by 
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(x3))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(tt))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(0))

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

(162)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
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   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(x3))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(tt))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
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   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(x3))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(tt))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(164)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
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   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
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   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(165) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, U42(z0, z1, z2), x1) -> c10(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(x1)) by 
   A__U42(tt, U42(x0, z1, z2), x3) -> c10(A__PLUS(mark(x3), U42(mark(x0), z1, z2)), MARK(x3))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(tt))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(0))

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

(166)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
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   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(tt))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
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   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(tt))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(168)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
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   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
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   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(169) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, plus(z0, z1), x1) -> c10(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) by 
   A__U42(tt, plus(x0, x1), x2) -> c10(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt))
   A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0))

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

(170)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
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   A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)))
   A__U42(tt, plus(x0, x1), x2) -> c10(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt))
   A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
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   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)))
   A__U42(tt, plus(x0, x1), x2) -> c10(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(tt))
   A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(172)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
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   A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2))
   A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1)))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2))
   A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(173) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, x0, U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) by 
   A__U42(tt, U11(z0, z1), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), a__U11(mark(z0), z1)), MARK(U11(x1, x2)))
   A__U42(tt, U12(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), a__U12(mark(z0))), MARK(U11(x1, x2)))
   A__U42(tt, isNat(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), a__isNat(z0)), MARK(U11(x1, x2)))
   A__U42(tt, U21(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), a__U21(mark(z0))), MARK(U11(x1, x2)))
   A__U42(tt, U31(z0, z1), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), a__U31(mark(z0), z1)), MARK(U11(x1, x2)))
   A__U42(tt, U41(z0, z1, z2), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(U11(x1, x2)))
   A__U42(tt, U42(z0, z1, z2), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), a__U42(mark(z0), z1, z2)), MARK(U11(x1, x2)))
   A__U42(tt, plus(z0, z1), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(U11(x1, x2)))
   A__U42(tt, tt, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), tt), MARK(U11(x1, x2)))
   A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2)))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2)))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2)))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)), MARK(U11(0, x2)))

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

(174)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
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   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
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   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
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   A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2))
   A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U42(tt, tt, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), tt), MARK(U11(x1, x2)))
   A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2)))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2)))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2)))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)), MARK(U11(0, x2)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
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   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2))
   A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U42(tt, tt, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), tt), MARK(U11(x1, x2)))
   A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2)))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2)))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2)))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)), MARK(U11(0, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(176)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
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   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2))
   A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2)))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2)))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2)))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0)))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
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   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2))
   A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2)))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2)))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2)))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(177) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, x0, U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) by 
   A__U42(tt, U11(z0, z1), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), a__U11(mark(z0), z1)), MARK(U12(x1)))
   A__U42(tt, U12(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), a__U12(mark(z0))), MARK(U12(x1)))
   A__U42(tt, isNat(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), a__isNat(z0)), MARK(U12(x1)))
   A__U42(tt, U21(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), a__U21(mark(z0))), MARK(U12(x1)))
   A__U42(tt, U31(z0, z1), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), a__U31(mark(z0), z1)), MARK(U12(x1)))
   A__U42(tt, U41(z0, z1, z2), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), a__U41(mark(z0), z1, z2)), MARK(U12(x1)))
   A__U42(tt, U42(z0, z1, z2), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), a__U42(mark(z0), z1, z2)), MARK(U12(x1)))
   A__U42(tt, plus(z0, z1), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(U12(x1)))
   A__U42(tt, tt, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), tt), MARK(U12(x1)))
   A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1)))
   A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1)))
   A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1)))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1))))
   A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0))))
   A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0))))
   A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0))))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1))))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1))))
   A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt)))
   A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0))))
   A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0)))
   A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1)))

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

(178)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
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   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2))
   A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2)))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2)))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2)))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U42(tt, tt, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), tt), MARK(U12(x1)))
   A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1)))
   A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1)))
   A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1)))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1))))
   A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0))))
   A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0))))
   A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0))))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1))))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1))))
   A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt)))
   A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0))))
   A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0)))
   A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
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   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
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   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
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   A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2))
   A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2)))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2)))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2)))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U42(tt, tt, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), tt), MARK(U12(x1)))
   A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1)))
   A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1)))
   A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1)))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1))))
   A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0))))
   A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0))))
   A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0))))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1))))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1))))
   A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt)))
   A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0))))
   A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0)))
   A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(180)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
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   A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2)))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2)))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2)))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1)))
   A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1)))
   A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1)))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1))))
   A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0))))
   A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0))))
   A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0))))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1))))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1))))
   A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt)))
   A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0))))
   A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0)))
   A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
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   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2))
   A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2)))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2)))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2)))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1)))
   A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1)))
   A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1)))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1))))
   A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0))))
   A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0))))
   A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0))))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1))))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1))))
   A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt)))
   A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0))))
   A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0)))
   A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(181) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) by 
   A__U42(tt, U11(z0, z1), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), a__U11(mark(z0), z1)), MARK(isNat(x1)))
   A__U42(tt, U12(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), a__U12(mark(z0))), MARK(isNat(x1)))
   A__U42(tt, isNat(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), a__isNat(z0)), MARK(isNat(x1)))
   A__U42(tt, U21(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), a__U21(mark(z0))), MARK(isNat(x1)))
   A__U42(tt, U31(z0, z1), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), a__U31(mark(z0), z1)), MARK(isNat(x1)))
   A__U42(tt, U41(z0, z1, z2), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), a__U41(mark(z0), z1, z2)), MARK(isNat(x1)))
   A__U42(tt, U42(z0, z1, z2), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), a__U42(mark(z0), z1, z2)), MARK(isNat(x1)))
   A__U42(tt, plus(z0, z1), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), a__plus(mark(z0), mark(z1))), MARK(isNat(x1)))
   A__U42(tt, tt, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1)))
   A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0))))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))

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

(182)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
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   A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2))
   A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2)))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2)))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2)))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1)))
   A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1)))
   A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1)))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1))))
   A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0))))
   A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0))))
   A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0))))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1))))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1))))
   A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt)))
   A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0))))
   A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0)))
   A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, tt, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1)))
   A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0))))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
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   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
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   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
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   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3))
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   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3))
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   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3))
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   A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
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   A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2))
   A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2)))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2)))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2)))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1)))
   A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1)))
   A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1)))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1))))
   A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0))))
   A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0))))
   A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0))))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1))))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1))))
   A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt)))
   A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0))))
   A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0)))
   A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, tt, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), tt), MARK(isNat(x1)))
   A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0))))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(184)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
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   A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0))))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0)))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
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   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2))
   A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2)))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2)))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2)))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1)))
   A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1)))
   A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1)))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1))))
   A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0))))
   A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0))))
   A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0))))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1))))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1))))
   A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt)))
   A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0))))
   A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0)))
   A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0))))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(185) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, x0, U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) by 
   A__U42(tt, U11(z0, z1), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), a__U11(mark(z0), z1)), MARK(U21(x1)))
   A__U42(tt, U12(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), a__U12(mark(z0))), MARK(U21(x1)))
   A__U42(tt, isNat(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), a__isNat(z0)), MARK(U21(x1)))
   A__U42(tt, U21(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), a__U21(mark(z0))), MARK(U21(x1)))
   A__U42(tt, U31(z0, z1), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), a__U31(mark(z0), z1)), MARK(U21(x1)))
   A__U42(tt, U41(z0, z1, z2), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), a__U41(mark(z0), z1, z2)), MARK(U21(x1)))
   A__U42(tt, U42(z0, z1, z2), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), a__U42(mark(z0), z1, z2)), MARK(U21(x1)))
   A__U42(tt, plus(z0, z1), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(U21(x1)))
   A__U42(tt, tt, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), tt), MARK(U21(x1)))
   A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1)))
   A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1)))
   A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1)))
   A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1))))
   A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0))))
   A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0))))
   A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0))))
   A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1))))
   A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1))))
   A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt)))
   A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0))))
   A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0)))
   A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1)))

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

(186)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
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   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2))
   A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2)))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2)))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2)))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1)))
   A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1)))
   A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1)))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1))))
   A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0))))
   A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0))))
   A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0))))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1))))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1))))
   A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt)))
   A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0))))
   A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0)))
   A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0))))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1)))
   A__U42(tt, tt, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), tt), MARK(U21(x1)))
   A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1)))
   A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1)))
   A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1)))
   A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1))))
   A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0))))
   A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0))))
   A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0))))
   A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1))))
   A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1))))
   A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt)))
   A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0))))
   A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0)))
   A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
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   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
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   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
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   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)))
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   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3))
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   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
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   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
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   A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2))
   A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2)))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2)))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2)))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1)))
   A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1)))
   A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1)))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1))))
   A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0))))
   A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0))))
   A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0))))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1))))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1))))
   A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt)))
   A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0))))
   A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0)))
   A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0))))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1)))
   A__U42(tt, tt, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), tt), MARK(U21(x1)))
   A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1)))
   A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1)))
   A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1)))
   A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1))))
   A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0))))
   A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0))))
   A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0))))
   A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1))))
   A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1))))
   A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt)))
   A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0))))
   A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0)))
   A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(188)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
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   A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2)))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2)))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1)))
   A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1)))
   A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1)))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1))))
   A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0))))
   A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0))))
   A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0))))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1))))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1))))
   A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt)))
   A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0))))
   A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0)))
   A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0))))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1)))
   A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1)))
   A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1)))
   A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1)))
   A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1))))
   A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0))))
   A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0))))
   A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0))))
   A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1))))
   A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1))))
   A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt)))
   A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0))))
   A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0)))
   A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1)))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
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   A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1))))
   A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0))))
   A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0))))
   A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0))))
   A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1))))
   A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1))))
   A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt)))
   A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0))))
   A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0)))
   A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(189) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, x0, U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) by 
   A__U42(tt, U11(z0, z1), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), a__U11(mark(z0), z1)), MARK(U31(x1, x2)))
   A__U42(tt, U12(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), a__U12(mark(z0))), MARK(U31(x1, x2)))
   A__U42(tt, isNat(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), a__isNat(z0)), MARK(U31(x1, x2)))
   A__U42(tt, U21(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), a__U21(mark(z0))), MARK(U31(x1, x2)))
   A__U42(tt, U31(z0, z1), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), a__U31(mark(z0), z1)), MARK(U31(x1, x2)))
   A__U42(tt, U41(z0, z1, z2), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(U31(x1, x2)))
   A__U42(tt, U42(z0, z1, z2), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), a__U42(mark(z0), z1, z2)), MARK(U31(x1, x2)))
   A__U42(tt, plus(z0, z1), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(U31(x1, x2)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), tt), MARK(U31(x1, x2)))
   A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2)))
   A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2)))
   A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2)))
   A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)), MARK(U31(0, x2)))

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

(190)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
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   A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0))))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1)))
   A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1)))
   A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1)))
   A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1)))
   A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1))))
   A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0))))
   A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0))))
   A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0))))
   A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1))))
   A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1))))
   A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt)))
   A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0))))
   A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0)))
   A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), tt), MARK(U31(x1, x2)))
   A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2)))
   A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2)))
   A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2)))
   A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)), MARK(U31(0, x2)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
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   A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt)))
   A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0))))
   A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0)))
   A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), tt), MARK(U31(x1, x2)))
   A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2)))
   A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2)))
   A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2)))
   A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)), MARK(U31(0, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(192)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
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   A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2)))
   A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2)))
   A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2)))
   A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
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   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
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   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U42(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(x3))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U42(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U42(mark(x0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U42(mark(x0), x1, x2)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(x2))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(x2))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(x2))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(x2))
   A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
   A__U42(tt, plus(x0, 0), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(x2))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2))
   A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2)))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2)))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2)))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1)))
   A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1)))
   A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1)))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1))))
   A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0))))
   A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0))))
   A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0))))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1))))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1))))
   A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt)))
   A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0))))
   A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0)))
   A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0))))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1)))
   A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1)))
   A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1)))
   A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1)))
   A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1))))
   A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0))))
   A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0))))
   A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0))))
   A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1))))
   A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1))))
   A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt)))
   A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0))))
   A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0)))
   A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2)))
   A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2)))
   A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2)))
   A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(193) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, x0, U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(U41(z0, z1, z2))) by 
   A__U42(tt, U11(z0, z1), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), a__U11(mark(z0), z1)), MARK(U41(x1, x2, x3)))
   A__U42(tt, U12(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), a__U12(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U42(tt, isNat(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), a__isNat(z0)), MARK(U41(x1, x2, x3)))
   A__U42(tt, U21(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), a__U21(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U42(tt, U31(z0, z1), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), a__U31(mark(z0), z1)), MARK(U41(x1, x2, x3)))
   A__U42(tt, U41(z0, z1, z2), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), a__U41(mark(z0), z1, z2)), MARK(U41(x1, x2, x3)))
   A__U42(tt, U42(z0, z1, z2), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), a__U42(mark(z0), z1, z2)), MARK(U41(x1, x2, x3)))
   A__U42(tt, plus(z0, z1), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(U41(x1, x2, x3)))
   A__U42(tt, tt, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), tt), MARK(U41(x1, x2, x3)))
   A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3)))
   A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3)))
   A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)), MARK(U41(0, x2, x3)))

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

(194)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
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   A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1))))
   A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1))))
   A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt)))
   A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0))))
   A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0)))
   A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2)))
   A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2)))
   A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2)))
   A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U42(tt, tt, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), tt), MARK(U41(x1, x2, x3)))
   A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3)))
   A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3)))
   A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)), MARK(U41(0, x2, x3)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
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   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
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   A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0))))
   A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1))))
   A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1))))
   A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt)))
   A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0))))
   A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0)))
   A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2)))
   A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2)))
   A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2)))
   A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U42(tt, tt, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), tt), MARK(U41(x1, x2, x3)))
   A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3)))
   A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3)))
   A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)), MARK(U41(0, x2, x3)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(196)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
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   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1))))
   A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt)))
   A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0))))
   A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0)))
   A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0))))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1)))
   A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1)))
   A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1)))
   A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1)))
   A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1))))
   A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0))))
   A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0))))
   A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0))))
   A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1))))
   A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1))))
   A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt)))
   A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0))))
   A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0)))
   A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2)))
   A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2)))
   A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2)))
   A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3)))
   A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3)))
   A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
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   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1))))
   A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt)))
   A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0))))
   A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0)))
   A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0))))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1)))
   A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1)))
   A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1)))
   A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1)))
   A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1))))
   A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0))))
   A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0))))
   A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0))))
   A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1))))
   A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1))))
   A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt)))
   A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0))))
   A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0)))
   A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2)))
   A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2)))
   A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2)))
   A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3)))
   A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3)))
   A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(197) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, x0, U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(U42(z0, z1, z2))) by 
   A__U42(tt, U11(z0, z1), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), a__U11(mark(z0), z1)), MARK(U42(x1, x2, x3)))
   A__U42(tt, U12(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), a__U12(mark(z0))), MARK(U42(x1, x2, x3)))
   A__U42(tt, isNat(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), a__isNat(z0)), MARK(U42(x1, x2, x3)))
   A__U42(tt, U21(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), a__U21(mark(z0))), MARK(U42(x1, x2, x3)))
   A__U42(tt, U31(z0, z1), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), a__U31(mark(z0), z1)), MARK(U42(x1, x2, x3)))
   A__U42(tt, U41(z0, z1, z2), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), a__U41(mark(z0), z1, z2)), MARK(U42(x1, x2, x3)))
   A__U42(tt, U42(z0, z1, z2), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), a__U42(mark(z0), z1, z2)), MARK(U42(x1, x2, x3)))
   A__U42(tt, plus(z0, z1), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), a__plus(mark(z0), mark(z1))), MARK(U42(x1, x2, x3)))
   A__U42(tt, tt, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), tt), MARK(U42(x1, x2, x3)))
   A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3)))
   A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2)))
   A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3)))
   A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3)))
   A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3)))
   A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)), MARK(U42(0, x2, x3)))

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

(198)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
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   A__U42(tt, plus(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(x2))
   A__U42(tt, plus(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(x2))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(x2))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(x2))
   A__U42(tt, plus(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(x2))
   A__U42(tt, plus(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(x2))
   A__U42(tt, plus(0, x1), x2) -> c10(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(x2))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U11(z0, z1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U12(z0)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(isNat(z0)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(U21(z0)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(U31(z0, z1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U41(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(z0, z1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(s(z0)))
   A__U42(tt, plus(x0, x1), x2) -> c10(MARK(x2))
   A__U42(tt, plus(x0, x1), tt) -> c10(A__PLUS(tt, a__plus(mark(x0), mark(x1))))
   A__U42(tt, plus(x0, x1), 0) -> c10(A__PLUS(0, a__plus(mark(x0), mark(x1))))
   A__U42(tt, s(z0), U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(U11(x1, x2)))
   A__U42(tt, 0, U11(x1, x2)) -> c10(A__PLUS(a__U11(mark(x1), x2), 0), MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(x1, z1)) -> c10(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(U11(x1, z1)))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U11(U11(z0, z1), x2)))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c10(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(U11(U12(z0), x2)))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c10(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(U11(isNat(z0), x2)))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c10(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(U11(U21(z0), x2)))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U11(U31(z0, z1), x2)))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U11(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c10(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U11(plus(z0, z1), x2)))
   A__U42(tt, x0, U11(tt, x2)) -> c10(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(U11(tt, x2)))
   A__U42(tt, x0, U11(s(z0), x2)) -> c10(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(U11(s(z0), x2)))
   A__U42(tt, tt, U11(x1, x2)) -> c10(MARK(U11(x1, x2)))
   A__U42(tt, x0, U11(0, x2)) -> c10(A__PLUS(a__U11(0, x2), mark(x0)))
   A__U42(tt, s(z0), U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(U12(x1)))
   A__U42(tt, 0, U12(x1)) -> c10(A__PLUS(a__U12(mark(x1)), 0), MARK(U12(x1)))
   A__U42(tt, x0, U12(x1)) -> c10(A__PLUS(U12(mark(x1)), mark(x0)), MARK(U12(x1)))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c10(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(U12(U11(z0, z1))))
   A__U42(tt, x0, U12(U12(z0))) -> c10(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(U12(U12(z0))))
   A__U42(tt, x0, U12(isNat(z0))) -> c10(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(U12(isNat(z0))))
   A__U42(tt, x0, U12(U21(z0))) -> c10(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(U12(U21(z0))))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c10(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(U12(U31(z0, z1))))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c10(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c10(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U12(plus(z0, z1))))
   A__U42(tt, x0, U12(tt)) -> c10(A__PLUS(a__U12(tt), mark(x0)), MARK(U12(tt)))
   A__U42(tt, x0, U12(s(z0))) -> c10(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(U12(s(z0))))
   A__U42(tt, x0, U12(0)) -> c10(A__PLUS(a__U12(0), mark(x0)), MARK(U12(0)))
   A__U42(tt, x0, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, tt, U12(x1)) -> c10(MARK(U12(x1)))
   A__U42(tt, s(z0), isNat(x1)) -> c10(A__PLUS(a__isNat(x1), s(mark(z0))), MARK(isNat(x1)))
   A__U42(tt, 0, isNat(x1)) -> c10(A__PLUS(a__isNat(x1), 0), MARK(isNat(x1)))
   A__U42(tt, x0, isNat(0)) -> c10(A__PLUS(tt, mark(x0)), MARK(isNat(0)))
   A__U42(tt, x0, isNat(plus(z0, z1))) -> c10(A__PLUS(a__U11(a__isNat(z0), z1), mark(x0)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, x0, isNat(s(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(isNat(s(z0))))
   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1)))
   A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1)))
   A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1)))
   A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1)))
   A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1))))
   A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0))))
   A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0))))
   A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0))))
   A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1))))
   A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1))))
   A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt)))
   A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0))))
   A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0)))
   A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2)))
   A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2)))
   A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2)))
   A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3)))
   A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3)))
   A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U42(tt, tt, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), tt), MARK(U42(x1, x2, x3)))
   A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3)))
   A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2)))
   A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3)))
   A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3)))
   A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3)))
   A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)), MARK(U42(0, x2, x3)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
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   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
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   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
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   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
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   A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3)))
   A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3)))
   A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3)))
   A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)), MARK(U42(0, x2, x3)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(200)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
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   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
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   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
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   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
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   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
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   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
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   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
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   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
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   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
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   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
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   A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2)))
   A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3)))
   A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3)))
   A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3)))
   A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2)))
   A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3)))
   A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3)))
   A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3)))
   A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1)))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
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   A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0))))
   A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0))))
   A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1))))
   A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1))))
   A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt)))
   A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0))))
   A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0)))
   A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2)))
   A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2)))
   A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2)))
   A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3)))
   A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3)))
   A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3)))
   A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2)))
   A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3)))
   A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3)))
   A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3)))
   A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(201) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, x0, plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) by 
   A__U42(tt, U11(z0, z1), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), a__U11(mark(z0), z1)), MARK(plus(x1, x2)))
   A__U42(tt, U12(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), a__U12(mark(z0))), MARK(plus(x1, x2)))
   A__U42(tt, isNat(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), a__isNat(z0)), MARK(plus(x1, x2)))
   A__U42(tt, U21(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), a__U21(mark(z0))), MARK(plus(x1, x2)))
   A__U42(tt, U31(z0, z1), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), a__U31(mark(z0), z1)), MARK(plus(x1, x2)))
   A__U42(tt, U41(z0, z1, z2), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), a__U41(mark(z0), z1, z2)), MARK(plus(x1, x2)))
   A__U42(tt, U42(z0, z1, z2), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), a__U42(mark(z0), z1, z2)), MARK(plus(x1, x2)))
   A__U42(tt, plus(z0, z1), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), a__plus(mark(z0), mark(z1))), MARK(plus(x1, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2)))
   A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0))))
   A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0))))
   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))

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

(202)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
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   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2)))
   A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0))))
   A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0))))
   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
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   A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2)))
   A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2)))
   A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2)))
   A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3)))
   A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3)))
   A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3)))
   A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2)))
   A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3)))
   A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3)))
   A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3)))
   A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), tt), MARK(plus(x1, x2)))
   A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0))))
   A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0))))
   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(204)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
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   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0)))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
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   A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3)))
   A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3)))
   A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2)))
   A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3)))
   A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3)))
   A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3)))
   A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0))))
   A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0))))
   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(205) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, x0, s(z0)) -> c10(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) by 
   A__U42(tt, U11(z0, z1), s(x1)) -> c10(A__PLUS(s(mark(x1)), a__U11(mark(z0), z1)), MARK(s(x1)))
   A__U42(tt, U12(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), a__U12(mark(z0))), MARK(s(x1)))
   A__U42(tt, isNat(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), a__isNat(z0)), MARK(s(x1)))
   A__U42(tt, U21(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), a__U21(mark(z0))), MARK(s(x1)))
   A__U42(tt, U31(z0, z1), s(x1)) -> c10(A__PLUS(s(mark(x1)), a__U31(mark(z0), z1)), MARK(s(x1)))
   A__U42(tt, U41(z0, z1, z2), s(x1)) -> c10(A__PLUS(s(mark(x1)), a__U41(mark(z0), z1, z2)), MARK(s(x1)))
   A__U42(tt, U42(z0, z1, z2), s(x1)) -> c10(A__PLUS(s(mark(x1)), a__U42(mark(z0), z1, z2)), MARK(s(x1)))
   A__U42(tt, plus(z0, z1), s(x1)) -> c10(A__PLUS(s(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(A__PLUS(s(mark(x1)), tt), MARK(s(x1)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))

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

(206)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
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   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, tt, s(x1)) -> c10(A__PLUS(s(mark(x1)), tt), MARK(s(x1)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
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   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3)))
   A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3)))
   A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3)))
   A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2)))
   A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3)))
   A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3)))
   A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3)))
   A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0))))
   A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0))))
   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, tt, s(x1)) -> c10(A__PLUS(s(mark(x1)), tt), MARK(s(x1)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(208)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
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   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
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   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
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   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)))
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   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3))
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   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
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   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
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   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0)))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
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   A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3)))
   A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3)))
   A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3)))
   A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2)))
   A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3)))
   A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3)))
   A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3)))
   A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0))))
   A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0))))
   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(209) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, x0, tt) -> c10(A__PLUS(tt, mark(x0))) by 
   A__U42(tt, U11(z0, z1), tt) -> c10(A__PLUS(tt, a__U11(mark(z0), z1)))
   A__U42(tt, U12(z0), tt) -> c10(A__PLUS(tt, a__U12(mark(z0))))
   A__U42(tt, isNat(z0), tt) -> c10(A__PLUS(tt, a__isNat(z0)))
   A__U42(tt, U21(z0), tt) -> c10(A__PLUS(tt, a__U21(mark(z0))))
   A__U42(tt, U31(z0, z1), tt) -> c10(A__PLUS(tt, a__U31(mark(z0), z1)))
   A__U42(tt, U41(z0, z1, z2), tt) -> c10(A__PLUS(tt, a__U41(mark(z0), z1, z2)))
   A__U42(tt, U42(z0, z1, z2), tt) -> c10(A__PLUS(tt, a__U42(mark(z0), z1, z2)))
   A__U42(tt, plus(z0, z1), tt) -> c10(A__PLUS(tt, a__plus(mark(z0), mark(z1))))
   A__U42(tt, tt, tt) -> c10(A__PLUS(tt, tt))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))

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

(210)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
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   A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0))))
   A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0))))
   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, tt) -> c10(A__PLUS(tt, tt))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
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   A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0)))
   A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2)))
   A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2)))
   A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2)))
   A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3)))
   A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3)))
   A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3)))
   A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2)))
   A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3)))
   A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3)))
   A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3)))
   A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0))))
   A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0))))
   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, tt) -> c10(A__PLUS(tt, tt))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(211) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U42(tt, tt, tt) -> c10(A__PLUS(tt, tt))

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

(212)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
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   A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0))))
   A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0))))
   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0)))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
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   A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt)))
   A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0))))
   A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0)))
   A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2)))
   A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2)))
   A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2)))
   A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3)))
   A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3)))
   A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3)))
   A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2)))
   A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3)))
   A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3)))
   A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3)))
   A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0))))
   A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0))))
   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(213) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, x0, 0) -> c10(A__PLUS(0, mark(x0))) by 
   A__U42(tt, U11(z0, z1), 0) -> c10(A__PLUS(0, a__U11(mark(z0), z1)))
   A__U42(tt, U12(z0), 0) -> c10(A__PLUS(0, a__U12(mark(z0))))
   A__U42(tt, isNat(z0), 0) -> c10(A__PLUS(0, a__isNat(z0)))
   A__U42(tt, U21(z0), 0) -> c10(A__PLUS(0, a__U21(mark(z0))))
   A__U42(tt, U31(z0, z1), 0) -> c10(A__PLUS(0, a__U31(mark(z0), z1)))
   A__U42(tt, U41(z0, z1, z2), 0) -> c10(A__PLUS(0, a__U41(mark(z0), z1, z2)))
   A__U42(tt, U42(z0, z1, z2), 0) -> c10(A__PLUS(0, a__U42(mark(z0), z1, z2)))
   A__U42(tt, plus(z0, z1), 0) -> c10(A__PLUS(0, a__plus(mark(z0), mark(z1))))
   A__U42(tt, tt, 0) -> c10(A__PLUS(0, tt))
   A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0))))
   A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0))

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

(214)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
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   A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0))))
   A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0))))
   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
   A__U42(tt, tt, 0) -> c10(A__PLUS(0, tt))
   A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0))))
   A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
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   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
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   A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1)))
   A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1)))
   A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1)))
   A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1)))
   A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1))))
   A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0))))
   A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0))))
   A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0))))
   A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1))))
   A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1))))
   A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt)))
   A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0))))
   A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0)))
   A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2)))
   A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2)))
   A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2)))
   A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3)))
   A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3)))
   A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3)))
   A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2)))
   A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3)))
   A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3)))
   A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3)))
   A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0))))
   A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0))))
   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
   A__U42(tt, tt, 0) -> c10(A__PLUS(0, tt))
   A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0))))
   A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(215) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U42(tt, tt, 0) -> c10(A__PLUS(0, tt))

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

(216)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
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   A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0))))
   A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0))))
   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
   A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0))))
   A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
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   A__U42(tt, x0, isNat(z0)) -> c10(A__PLUS(isNat(z0), mark(x0)), MARK(isNat(z0)))
   A__U42(tt, tt, isNat(x1)) -> c10(MARK(isNat(x1)))
   A__U42(tt, s(z0), U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), s(mark(z0))), MARK(U21(x1)))
   A__U42(tt, 0, U21(x1)) -> c10(A__PLUS(a__U21(mark(x1)), 0), MARK(U21(x1)))
   A__U42(tt, x0, U21(x1)) -> c10(A__PLUS(U21(mark(x1)), mark(x0)), MARK(U21(x1)))
   A__U42(tt, x0, U21(U11(z0, z1))) -> c10(A__PLUS(a__U21(a__U11(mark(z0), z1)), mark(x0)), MARK(U21(U11(z0, z1))))
   A__U42(tt, x0, U21(U12(z0))) -> c10(A__PLUS(a__U21(a__U12(mark(z0))), mark(x0)), MARK(U21(U12(z0))))
   A__U42(tt, x0, U21(isNat(z0))) -> c10(A__PLUS(a__U21(a__isNat(z0)), mark(x0)), MARK(U21(isNat(z0))))
   A__U42(tt, x0, U21(U21(z0))) -> c10(A__PLUS(a__U21(a__U21(mark(z0))), mark(x0)), MARK(U21(U21(z0))))
   A__U42(tt, x0, U21(U31(z0, z1))) -> c10(A__PLUS(a__U21(a__U31(mark(z0), z1)), mark(x0)), MARK(U21(U31(z0, z1))))
   A__U42(tt, x0, U21(U41(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, x0, U21(U42(z0, z1, z2))) -> c10(A__PLUS(a__U21(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, x0, U21(plus(z0, z1))) -> c10(A__PLUS(a__U21(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(U21(plus(z0, z1))))
   A__U42(tt, x0, U21(tt)) -> c10(A__PLUS(a__U21(tt), mark(x0)), MARK(U21(tt)))
   A__U42(tt, x0, U21(s(z0))) -> c10(A__PLUS(a__U21(s(mark(z0))), mark(x0)), MARK(U21(s(z0))))
   A__U42(tt, x0, U21(0)) -> c10(A__PLUS(a__U21(0), mark(x0)), MARK(U21(0)))
   A__U42(tt, x0, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, tt, U21(x1)) -> c10(MARK(U21(x1)))
   A__U42(tt, s(z0), U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), s(mark(z0))), MARK(U31(x1, x2)))
   A__U42(tt, 0, U31(x1, x2)) -> c10(A__PLUS(a__U31(mark(x1), x2), 0), MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(x1, z1)) -> c10(A__PLUS(U31(mark(x1), z1), mark(x0)), MARK(U31(x1, z1)))
   A__U42(tt, x0, U31(U11(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U11(mark(z0), z1), x2), mark(x0)), MARK(U31(U11(z0, z1), x2)))
   A__U42(tt, x0, U31(U12(z0), x2)) -> c10(A__PLUS(a__U31(a__U12(mark(z0)), x2), mark(x0)), MARK(U31(U12(z0), x2)))
   A__U42(tt, x0, U31(isNat(z0), x2)) -> c10(A__PLUS(a__U31(a__isNat(z0), x2), mark(x0)), MARK(U31(isNat(z0), x2)))
   A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2)))
   A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3)))
   A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3)))
   A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3)))
   A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2)))
   A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3)))
   A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3)))
   A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3)))
   A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0))))
   A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0))))
   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
   A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0))))
   A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(217) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, U11(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) by 
   A__U42(tt, U11(x0, z1), x2) -> c11(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(U11(x0, z1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1)))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1)))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1)), MARK(U11(0, x1)))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))

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

(218)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
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   A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3)))
   A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3)))
   A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3)))
   A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2)))
   A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3)))
   A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3)))
   A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3)))
   A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0))))
   A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0))))
   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
   A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0))))
   A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0))
   A__U42(tt, U11(x0, z1), x2) -> c11(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(U11(x0, z1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1)))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1)))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1)), MARK(U11(0, x1)))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
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   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
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   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
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   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
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   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
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   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
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   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
   A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0))))
   A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0))
   A__U42(tt, U11(x0, z1), x2) -> c11(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(U11(x0, z1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1)))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1)))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1)), MARK(U11(0, x1)))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(220)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
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   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
   A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0))))
   A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1)))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1)))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1)))
   A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
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   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
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   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
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   A__U42(tt, x0, U31(U21(z0), x2)) -> c10(A__PLUS(a__U31(a__U21(mark(z0)), x2), mark(x0)), MARK(U31(U21(z0), x2)))
   A__U42(tt, x0, U31(U31(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__U31(mark(z0), z1), x2), mark(x0)), MARK(U31(U31(z0, z1), x2)))
   A__U42(tt, x0, U31(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__U31(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(U31(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, U31(plus(z0, z1), x2)) -> c10(A__PLUS(a__U31(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(U31(plus(z0, z1), x2)))
   A__U42(tt, x0, U31(tt, x2)) -> c10(A__PLUS(a__U31(tt, x2), mark(x0)), MARK(U31(tt, x2)))
   A__U42(tt, x0, U31(s(z0), x2)) -> c10(A__PLUS(a__U31(s(mark(z0)), x2), mark(x0)), MARK(U31(s(z0), x2)))
   A__U42(tt, tt, U31(x1, x2)) -> c10(MARK(U31(x1, x2)))
   A__U42(tt, x0, U31(0, x2)) -> c10(A__PLUS(a__U31(0, x2), mark(x0)))
   A__U42(tt, s(z0), U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), s(mark(z0))), MARK(U41(x1, x2, x3)))
   A__U42(tt, 0, U41(x1, x2, x3)) -> c10(A__PLUS(a__U41(mark(x1), x2, x3), 0), MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(x1, z1, z2)) -> c10(A__PLUS(U41(mark(x1), z1, z2), mark(x0)), MARK(U41(x1, z1, z2)))
   A__U42(tt, x0, U41(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U12(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U41(U12(z0), x2, x3)))
   A__U42(tt, x0, U41(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__isNat(z0), x2, x3), mark(x0)), MARK(U41(isNat(z0), x2, x3)))
   A__U42(tt, x0, U41(U21(z0), x2, x3)) -> c10(A__PLUS(a__U41(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U41(U21(z0), x2, x3)))
   A__U42(tt, x0, U41(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U41(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U41(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U41(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U41(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U41(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U41(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U41(tt, x2, x3)) -> c10(A__PLUS(a__U41(tt, x2, x3), mark(x0)), MARK(U41(tt, x2, x3)))
   A__U42(tt, x0, U41(s(z0), x2, x3)) -> c10(A__PLUS(a__U41(s(mark(z0)), x2, x3), mark(x0)), MARK(U41(s(z0), x2, x3)))
   A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3)))
   A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2)))
   A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3)))
   A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3)))
   A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3)))
   A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0))))
   A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0))))
   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
   A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0))))
   A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1)))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1)))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1)))
   A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(221) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, U12(z0), x1) -> c11(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) by 
   A__U42(tt, U12(x0), x1) -> c11(A__PLUS(mark(x1), U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0))))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1))))
   A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt)))
   A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0)))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0)))

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

(222)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
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   A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
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   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
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   A__U42(tt, tt, U41(x1, x2, x3)) -> c10(MARK(U41(x1, x2, x3)))
   A__U42(tt, x0, U41(0, x2, x3)) -> c10(A__PLUS(a__U41(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), s(mark(z0))), MARK(U42(x1, x2, x3)))
   A__U42(tt, 0, U42(x1, x2, x3)) -> c10(A__PLUS(a__U42(mark(x1), x2, x3), 0), MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(x1, z1, z2)) -> c10(A__PLUS(U42(mark(x1), z1, z2), mark(x0)), MARK(U42(x1, z1, z2)))
   A__U42(tt, x0, U42(U11(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U11(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U11(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U12(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U12(mark(z0)), x2, x3), mark(x0)), MARK(U42(U12(z0), x2, x3)))
   A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3)))
   A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3)))
   A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0))))
   A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0))))
   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
   A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0))))
   A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1)))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1)))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1)))
   A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1)))
   A__U42(tt, U12(x0), x1) -> c11(A__PLUS(mark(x1), U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0))))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1))))
   A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt)))
   A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0)))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(224)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
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   A__U42(tt, x0, U42(isNat(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__isNat(z0), x2, x3), mark(x0)), MARK(U42(isNat(z0), x2, x3)))
   A__U42(tt, x0, U42(U21(z0), x2, x3)) -> c10(A__PLUS(a__U42(a__U21(mark(z0)), x2, x3), mark(x0)), MARK(U42(U21(z0), x2, x3)))
   A__U42(tt, x0, U42(U31(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__U31(mark(z0), z1), x2, x3), mark(x0)), MARK(U42(U31(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(U41(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U41(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U41(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(U42(z0, z1, z2), x2, x3)) -> c10(A__PLUS(a__U42(a__U42(mark(z0), z1, z2), x2, x3), mark(x0)), MARK(U42(U42(z0, z1, z2), x2, x3)))
   A__U42(tt, x0, U42(plus(z0, z1), x2, x3)) -> c10(A__PLUS(a__U42(a__plus(mark(z0), mark(z1)), x2, x3), mark(x0)), MARK(U42(plus(z0, z1), x2, x3)))
   A__U42(tt, x0, U42(tt, x2, x3)) -> c10(A__PLUS(a__U42(tt, x2, x3), mark(x0)), MARK(U42(tt, x2, x3)))
   A__U42(tt, x0, U42(s(z0), x2, x3)) -> c10(A__PLUS(a__U42(s(mark(z0)), x2, x3), mark(x0)), MARK(U42(s(z0), x2, x3)))
   A__U42(tt, tt, U42(x1, x2, x3)) -> c10(MARK(U42(x1, x2, x3)))
   A__U42(tt, x0, U42(0, x2, x3)) -> c10(A__PLUS(a__U42(0, x2, x3), mark(x0)))
   A__U42(tt, s(z0), plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), s(mark(z0))), MARK(plus(x1, x2)))
   A__U42(tt, 0, plus(x1, x2)) -> c10(A__PLUS(a__plus(mark(x1), mark(x2)), 0), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0))))
   A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0))))
   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
   A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0))))
   A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1)))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1)))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1)))
   A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0))))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1))))
   A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt)))
   A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0)))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
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   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
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   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
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   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)))
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   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(x3))
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   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
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   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
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   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
   A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0))))
   A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1)))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1)))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1)))
   A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0))))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1))))
   A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt)))
   A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0)))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(225) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) by 
   A__U42(tt, isNat(0), x1) -> c11(A__PLUS(mark(x1), tt), MARK(isNat(0)))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0))))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0)))

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

(226)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
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   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
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   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
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   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
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   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
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   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
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   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
   A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0))))
   A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1)))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1)))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1)))
   A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0))))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1))))
   A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt)))
   A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0)))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0)))
   A__U42(tt, isNat(0), x1) -> c11(A__PLUS(mark(x1), tt), MARK(isNat(0)))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0))))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
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   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
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   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
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   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
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   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(x3))
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   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
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   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
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   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c10(MARK(x3))
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   A__U42(tt, plus(x0, tt), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(x2))
   A__U42(tt, plus(x0, s(z0)), x2) -> c10(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(x2))
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   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
   A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0))))
   A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1)))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1)))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1)))
   A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0))))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1))))
   A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt)))
   A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0)))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0)))
   A__U42(tt, isNat(0), x1) -> c11(A__PLUS(mark(x1), tt), MARK(isNat(0)))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0))))
   A__U42(tt, isNat(z0), x1) -> c11(A__PLUS(mark(x1), isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(228)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
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   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
   A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0))))
   A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1)))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1)))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1)))
   A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0))))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1))))
   A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt)))
   A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0)))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0)))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0))))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0)))
   A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
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   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
   A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0))))
   A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1)))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1)))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1)))
   A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0))))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1))))
   A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt)))
   A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0)))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0)))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0))))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0)))
   A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(229) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, U21(z0), x1) -> c11(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) by 
   A__U42(tt, U21(x0), x1) -> c11(A__PLUS(mark(x1), U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1))))
   A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0))))
   A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0))))
   A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0))))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1))))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1))))
   A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt)))
   A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0))))
   A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0)))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0)))

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

(230)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
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   A__U42(tt, x0, plus(x1, x2)) -> c10(A__PLUS(plus(mark(x1), mark(x2)), mark(x0)), MARK(plus(x1, x2)))
   A__U42(tt, x0, plus(x1, U11(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U11(mark(z0), z1)), mark(x0)), MARK(plus(x1, U11(z0, z1))))
   A__U42(tt, x0, plus(x1, U12(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U12(mark(z0))), mark(x0)), MARK(plus(x1, U12(z0))))
   A__U42(tt, x0, plus(x1, isNat(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__isNat(z0)), mark(x0)), MARK(plus(x1, isNat(z0))))
   A__U42(tt, x0, plus(x1, U21(z0))) -> c10(A__PLUS(a__plus(mark(x1), a__U21(mark(z0))), mark(x0)), MARK(plus(x1, U21(z0))))
   A__U42(tt, x0, plus(x1, U31(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__U31(mark(z0), z1)), mark(x0)), MARK(plus(x1, U31(z0, z1))))
   A__U42(tt, x0, plus(x1, U41(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U41(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U41(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, U42(z0, z1, z2))) -> c10(A__PLUS(a__plus(mark(x1), a__U42(mark(z0), z1, z2)), mark(x0)), MARK(plus(x1, U42(z0, z1, z2))))
   A__U42(tt, x0, plus(x1, plus(z0, z1))) -> c10(A__PLUS(a__plus(mark(x1), a__plus(mark(z0), mark(z1))), mark(x0)), MARK(plus(x1, plus(z0, z1))))
   A__U42(tt, x0, plus(x1, tt)) -> c10(A__PLUS(a__plus(mark(x1), tt), mark(x0)), MARK(plus(x1, tt)))
   A__U42(tt, x0, plus(x1, s(z0))) -> c10(A__PLUS(a__plus(mark(x1), s(mark(z0))), mark(x0)), MARK(plus(x1, s(z0))))
   A__U42(tt, x0, plus(x1, 0)) -> c10(A__PLUS(a__plus(mark(x1), 0), mark(x0)), MARK(plus(x1, 0)))
   A__U42(tt, x0, plus(U11(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U11(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U11(z0, z1), x2)))
   A__U42(tt, x0, plus(U12(z0), x2)) -> c10(A__PLUS(a__plus(a__U12(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U12(z0), x2)))
   A__U42(tt, x0, plus(isNat(z0), x2)) -> c10(A__PLUS(a__plus(a__isNat(z0), mark(x2)), mark(x0)), MARK(plus(isNat(z0), x2)))
   A__U42(tt, x0, plus(U21(z0), x2)) -> c10(A__PLUS(a__plus(a__U21(mark(z0)), mark(x2)), mark(x0)), MARK(plus(U21(z0), x2)))
   A__U42(tt, x0, plus(U31(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__U31(mark(z0), z1), mark(x2)), mark(x0)), MARK(plus(U31(z0, z1), x2)))
   A__U42(tt, x0, plus(U41(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U41(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U41(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(U42(z0, z1, z2), x2)) -> c10(A__PLUS(a__plus(a__U42(mark(z0), z1, z2), mark(x2)), mark(x0)), MARK(plus(U42(z0, z1, z2), x2)))
   A__U42(tt, x0, plus(plus(z0, z1), x2)) -> c10(A__PLUS(a__plus(a__plus(mark(z0), mark(z1)), mark(x2)), mark(x0)), MARK(plus(plus(z0, z1), x2)))
   A__U42(tt, x0, plus(tt, x2)) -> c10(A__PLUS(a__plus(tt, mark(x2)), mark(x0)), MARK(plus(tt, x2)))
   A__U42(tt, x0, plus(s(z0), x2)) -> c10(A__PLUS(a__plus(s(mark(z0)), mark(x2)), mark(x0)), MARK(plus(s(z0), x2)))
   A__U42(tt, x0, plus(0, x2)) -> c10(A__PLUS(a__plus(0, mark(x2)), mark(x0)), MARK(plus(0, x2)))
   A__U42(tt, tt, plus(x1, x2)) -> c10(MARK(plus(x1, x2)))
   A__U42(tt, s(z0), s(x1)) -> c10(A__PLUS(s(mark(x1)), s(mark(z0))), MARK(s(x1)))
   A__U42(tt, 0, s(x1)) -> c10(A__PLUS(s(mark(x1)), 0), MARK(s(x1)))
   A__U42(tt, x0, s(U11(z0, z1))) -> c10(A__PLUS(s(a__U11(mark(z0), z1)), mark(x0)), MARK(s(U11(z0, z1))))
   A__U42(tt, x0, s(U12(z0))) -> c10(A__PLUS(s(a__U12(mark(z0))), mark(x0)), MARK(s(U12(z0))))
   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
   A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0))))
   A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1)))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1)))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1)))
   A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0))))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1))))
   A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt)))
   A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0)))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0)))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0))))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0)))
   A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0)))
   A__U42(tt, U21(x0), x1) -> c11(A__PLUS(mark(x1), U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1))))
   A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0))))
   A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0))))
   A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0))))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1))))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1))))
   A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt)))
   A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0))))
   A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0)))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
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   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
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   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
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   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
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   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
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   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
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   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
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   A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(232)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
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   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
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   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
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   A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0))))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0)))
   A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1))))
   A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0))))
   A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0))))
   A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0))))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1))))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1))))
   A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt)))
   A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0))))
   A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0)))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
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   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
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   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
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   A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0)))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0))))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0)))
   A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1))))
   A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0))))
   A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0))))
   A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0))))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1))))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1))))
   A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt)))
   A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0))))
   A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0)))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(233) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, U31(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) by 
   A__U42(tt, U31(x0, z1), x2) -> c11(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(U31(x0, z1)))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1)))
   A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1)))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1)))
   A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1)))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1)))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1)))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1)))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1)))
   A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1)))
   A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1)))
   A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1)), MARK(U31(0, x1)))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))

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

(234)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
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   A__U42(tt, x0, s(isNat(z0))) -> c10(A__PLUS(s(a__isNat(z0)), mark(x0)), MARK(s(isNat(z0))))
   A__U42(tt, x0, s(U21(z0))) -> c10(A__PLUS(s(a__U21(mark(z0))), mark(x0)), MARK(s(U21(z0))))
   A__U42(tt, x0, s(U31(z0, z1))) -> c10(A__PLUS(s(a__U31(mark(z0), z1)), mark(x0)), MARK(s(U31(z0, z1))))
   A__U42(tt, x0, s(U41(z0, z1, z2))) -> c10(A__PLUS(s(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(s(U41(z0, z1, z2))))
   A__U42(tt, x0, s(U42(z0, z1, z2))) -> c10(A__PLUS(s(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(s(U42(z0, z1, z2))))
   A__U42(tt, x0, s(plus(z0, z1))) -> c10(A__PLUS(s(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(s(plus(z0, z1))))
   A__U42(tt, x0, s(tt)) -> c10(A__PLUS(s(tt), mark(x0)), MARK(s(tt)))
   A__U42(tt, x0, s(s(z0))) -> c10(A__PLUS(s(s(mark(z0))), mark(x0)), MARK(s(s(z0))))
   A__U42(tt, x0, s(0)) -> c10(A__PLUS(s(0), mark(x0)), MARK(s(0)))
   A__U42(tt, x0, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, tt, s(x1)) -> c10(MARK(s(x1)))
   A__U42(tt, s(z0), tt) -> c10(A__PLUS(tt, s(mark(z0))))
   A__U42(tt, 0, tt) -> c10(A__PLUS(tt, 0))
   A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0))))
   A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1)))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1)))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1)))
   A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0))))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1))))
   A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt)))
   A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0)))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0)))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0))))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0)))
   A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1))))
   A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0))))
   A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0))))
   A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0))))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1))))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1))))
   A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt)))
   A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0))))
   A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0)))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0)))
   A__U42(tt, U31(x0, z1), x2) -> c11(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(U31(x0, z1)))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1)))
   A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1)))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1)))
   A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1)))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1)))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1)))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1)))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1)))
   A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1)))
   A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1)))
   A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1)), MARK(U31(0, x1)))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
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   A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0)))
   A__U42(tt, U31(x0, z1), x2) -> c11(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(U31(x0, z1)))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1)))
   A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1)))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1)))
   A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1)))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1)))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1)))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1)))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1)))
   A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1)))
   A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1)))
   A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1)), MARK(U31(0, x1)))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(236)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
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   A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1))))
   A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt)))
   A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0)))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0)))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0))))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0)))
   A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1))))
   A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0))))
   A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0))))
   A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0))))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1))))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1))))
   A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt)))
   A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0))))
   A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0)))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0)))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1)))
   A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1)))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1)))
   A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1)))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1)))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1)))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1)))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1)))
   A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1)))
   A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1)))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1)))
   A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
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   A__U42(tt, s(z0), 0) -> c10(A__PLUS(0, s(mark(z0))))
   A__U42(tt, 0, 0) -> c10(A__PLUS(0, 0))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(U11(U11(z0, z1), x1)))
   A__U42(tt, U11(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(U11(U12(z0), x1)))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(U11(isNat(z0), x1)))
   A__U42(tt, U11(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(U11(U21(z0), x1)))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(U11(U31(z0, z1), x1)))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(U11(U41(z0, z1, z2), x1)))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(U11(U42(z0, z1, z2), x1)))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(U11(plus(z0, z1), x1)))
   A__U42(tt, U11(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(U11(tt, x1)))
   A__U42(tt, U11(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(U11(s(z0), x1)))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), tt) -> c11(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, x1), 0) -> c11(A__PLUS(0, a__U11(mark(x0), x1)), MARK(U11(x0, x1)))
   A__U42(tt, U11(x0, z1), x2) -> c11(MARK(U11(x0, z1)))
   A__U42(tt, U11(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U11(0, x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(U12(U11(z0, z1))))
   A__U42(tt, U12(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(U12(U12(z0))))
   A__U42(tt, U12(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(U12(isNat(z0))))
   A__U42(tt, U12(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(U12(U21(z0))))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(U12(U31(z0, z1))))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(U12(U41(z0, z1, z2))))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(U12(U42(z0, z1, z2))))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(U12(plus(z0, z1))))
   A__U42(tt, U12(tt), x1) -> c11(A__PLUS(mark(x1), a__U12(tt)), MARK(U12(tt)))
   A__U42(tt, U12(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(U12(s(z0))))
   A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0)))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0)))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0))))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0)))
   A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1))))
   A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0))))
   A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0))))
   A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0))))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1))))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1))))
   A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt)))
   A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0))))
   A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0)))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0)))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1)))
   A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1)))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1)))
   A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1)))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1)))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1)))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1)))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1)))
   A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1)))
   A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1)))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1)))
   A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(237) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, U41(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2))) by 
   A__U42(tt, U41(x0, z1, z2), x3) -> c11(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(U41(x0, z1, z2)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2)))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2)))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2)))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2)))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2)))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2)))
   A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2)))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2)))
   A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(U41(0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))

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

(238)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U12(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U12(tt), x1) -> c10(A__PLUS(mark(x1), a__U12(tt)), MARK(x1))
   A__U42(tt, U12(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1))
   A__U42(tt, U12(0), x1) -> c10(A__PLUS(mark(x1), a__U12(0)), MARK(x1))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U12(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U12(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U12(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0)))
   A__U42(tt, U12(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U12(x0), tt) -> c10(A__PLUS(tt, a__U12(mark(x0))))
   A__U42(tt, U12(x0), 0) -> c10(A__PLUS(0, a__U12(mark(x0))))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1))
   A__U42(tt, isNat(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1)))
   A__U42(tt, isNat(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(U41(z0, z1, z2)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(U42(z0, z1, z2)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1)))
   A__U42(tt, isNat(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0)))
   A__U42(tt, isNat(0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(z0), x1) -> c10(MARK(x1))
   A__U42(tt, isNat(x0), tt) -> c10(A__PLUS(tt, a__isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c10(A__PLUS(0, a__isNat(x0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U21(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1))
   A__U42(tt, U21(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(x1))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1))
   A__U42(tt, U21(tt), x1) -> c10(A__PLUS(mark(x1), a__U21(tt)), MARK(x1))
   A__U42(tt, U21(s(z0)), x1) -> c10(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1))
   A__U42(tt, U21(0), x1) -> c10(A__PLUS(mark(x1), a__U21(0)), MARK(x1))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1)))
   A__U42(tt, U21(x0), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0)))
   A__U42(tt, U21(x0), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U41(z0, z1, z2)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U42(z0, z1, z2)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1)))
   A__U42(tt, U21(x0), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0)))
   A__U42(tt, U21(x0), x1) -> c10(MARK(x1))
   A__U42(tt, U21(x0), tt) -> c10(A__PLUS(tt, a__U21(mark(x0))))
   A__U42(tt, U21(x0), 0) -> c10(A__PLUS(0, a__U21(mark(x0))))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U31(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U31(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2))
   A__U42(tt, U31(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U31(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U31(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U31(x0, x1), tt) -> c10(A__PLUS(tt, a__U31(mark(x0), x1)))
   A__U42(tt, U31(x0, x1), 0) -> c10(A__PLUS(0, a__U31(mark(x0), x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(x3))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(x3))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(x3))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3))
   A__U42(tt, U41(tt, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(x3))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(isNat(z0)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
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   A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0))))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0)))
   A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1))))
   A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0))))
   A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0))))
   A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0))))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1))))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1))))
   A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt)))
   A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0))))
   A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0)))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0)))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1)))
   A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1)))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1)))
   A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1)))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1)))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1)))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1)))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1)))
   A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1)))
   A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1)))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1)))
   A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c11(A__PLUS(mark(x3), U41(mark(x0), z1, z2)), MARK(U41(x0, z1, z2)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2)))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2)))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2)))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2)))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2)))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2)))
   A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2)))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2)))
   A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(U41(0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
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   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2)))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2)))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2)))
   A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2)))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2)))
   A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(U41(0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(240)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
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   A__U42(tt, U12(0), x1) -> c11(A__PLUS(mark(x1), a__U12(0)), MARK(U12(0)))
   A__U42(tt, U12(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), tt) -> c11(A__PLUS(tt, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), 0) -> c11(A__PLUS(0, a__U12(mark(x0))), MARK(U12(x0)))
   A__U42(tt, U12(x0), x1) -> c11(MARK(U12(x0)))
   A__U42(tt, isNat(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(isNat(plus(z0, z1))))
   A__U42(tt, isNat(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(isNat(s(z0))))
   A__U42(tt, isNat(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0)))
   A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1))))
   A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0))))
   A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0))))
   A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0))))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1))))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1))))
   A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt)))
   A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0))))
   A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0)))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0)))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1)))
   A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1)))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1)))
   A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1)))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1)))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1)))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1)))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1)))
   A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1)))
   A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1)))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1)))
   A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2)))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2)))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2)))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2)))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2)))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2)))
   A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2)))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2)))
   A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
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   A__U42(tt, U41(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U41(0, x1, x2)), MARK(x3))
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   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U12(z0)))
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   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(plus(z0, z1)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(s(z0)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c10(MARK(x3))
   A__U42(tt, U41(x0, x1, x2), tt) -> c10(A__PLUS(tt, a__U41(mark(x0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c10(A__PLUS(0, a__U41(mark(x0), x1, x2)))
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   A__U42(tt, U42(s(z0), x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(x3))
   A__U42(tt, U42(0, x1, x2), x3) -> c10(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(x3))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U11(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U12(z0)))
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   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U21(z0)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U31(z0, z1)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U41(z0, z1, z2)))
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   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1)))
   A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2)))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2)))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2)))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2)))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2)))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2)))
   A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2)))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2)))
   A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(241) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, U42(z0, z1, z2), x1) -> c11(A__PLUS(mark(x1), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2))) by 
   A__U42(tt, U42(x0, z1, z2), x3) -> c11(A__PLUS(mark(x3), U42(mark(x0), z1, z2)), MARK(U42(x0, z1, z2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2)))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2)))
   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2)))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2)))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2)))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2)))
   A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2)))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2)))
   A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(U42(0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))

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

(242)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
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   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2)))
   A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c11(A__PLUS(mark(x3), U42(mark(x0), z1, z2)), MARK(U42(x0, z1, z2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2)))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2)))
   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2)))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2)))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2)))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2)))
   A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2)))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2)))
   A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2)), MARK(U42(0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
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   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(244)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
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   A__U42(tt, isNat(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), tt) -> c11(A__PLUS(tt, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(x0), 0) -> c11(A__PLUS(0, a__isNat(x0)), MARK(isNat(x0)))
   A__U42(tt, isNat(0), x1) -> c11(MARK(isNat(0)))
   A__U42(tt, isNat(z0), x1) -> c11(MARK(isNat(z0)))
   A__U42(tt, U21(U11(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(U21(U11(z0, z1))))
   A__U42(tt, U21(U12(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(U21(U12(z0))))
   A__U42(tt, U21(isNat(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(U21(isNat(z0))))
   A__U42(tt, U21(U21(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(U21(U21(z0))))
   A__U42(tt, U21(U31(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(U21(U31(z0, z1))))
   A__U42(tt, U21(U41(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1, z2))), MARK(U21(U41(z0, z1, z2))))
   A__U42(tt, U21(U42(z0, z1, z2)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__U42(mark(z0), z1, z2))), MARK(U21(U42(z0, z1, z2))))
   A__U42(tt, U21(plus(z0, z1)), x1) -> c11(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(U21(plus(z0, z1))))
   A__U42(tt, U21(tt), x1) -> c11(A__PLUS(mark(x1), a__U21(tt)), MARK(U21(tt)))
   A__U42(tt, U21(s(z0)), x1) -> c11(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(U21(s(z0))))
   A__U42(tt, U21(0), x1) -> c11(A__PLUS(mark(x1), a__U21(0)), MARK(U21(0)))
   A__U42(tt, U21(x0), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0)))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1)))
   A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1)))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1)))
   A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1)))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1)))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1)))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1)))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1)))
   A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1)))
   A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1)))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1)))
   A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2)))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2)))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2)))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2)))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2)))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2)))
   A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2)))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2)))
   A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2)))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2)))
   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2)))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2)))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2)))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2)))
   A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2)))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2)))
   A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
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   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1)))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1)))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1)))
   A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1)))
   A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1)))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1)))
   A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2)))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2)))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2)))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2)))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2)))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2)))
   A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2)))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2)))
   A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2)))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2)))
   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2)))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2)))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2)))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2)))
   A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2)))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2)))
   A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(245) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, plus(z0, z1), x1) -> c11(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) by 
   A__U42(tt, plus(x0, x1), x2) -> c11(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1))))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0))))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0))))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0))))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1))))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2))))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2))))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1)))
   A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1)))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1)))
   A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1)))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1)))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1)))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1)))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))

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

(246)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
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   A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
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   A__U42(tt, U21(x0), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), tt) -> c11(A__PLUS(tt, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), 0) -> c11(A__PLUS(0, a__U21(mark(x0))), MARK(U21(x0)))
   A__U42(tt, U21(x0), x1) -> c11(MARK(U21(x0)))
   A__U42(tt, U31(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(U31(U11(z0, z1), x1)))
   A__U42(tt, U31(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(U31(U12(z0), x1)))
   A__U42(tt, U31(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(U31(isNat(z0), x1)))
   A__U42(tt, U31(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(U31(U21(z0), x1)))
   A__U42(tt, U31(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(U31(U31(z0, z1), x1)))
   A__U42(tt, U31(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1, z2), x1)), MARK(U31(U41(z0, z1, z2), x1)))
   A__U42(tt, U31(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__U42(mark(z0), z1, z2), x1)), MARK(U31(U42(z0, z1, z2), x1)))
   A__U42(tt, U31(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(U31(plus(z0, z1), x1)))
   A__U42(tt, U31(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(U31(tt, x1)))
   A__U42(tt, U31(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(U31(s(z0), x1)))
   A__U42(tt, U31(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1)))
   A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2)))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2)))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2)))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2)))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2)))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2)))
   A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2)))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2)))
   A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2)))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2)))
   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2)))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2)))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2)))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2)))
   A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2)))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2)))
   A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2)))
   A__U42(tt, plus(x0, x1), x2) -> c11(A__PLUS(mark(x2), plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1))))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0))))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0))))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0))))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1))))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2))))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2))))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1)))
   A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1)))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1)))
   A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1)))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1)))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1)))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1)))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(248)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
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   A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1)))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
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   A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1)))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(249) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, x0, U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) by 
   A__U42(tt, U11(z0, z1), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, tt, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), tt), MARK(tt))
   A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0), MARK(0))
   A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0))

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

(250)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
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   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2)))
   A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1))))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0))))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0))))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0))))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1))))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2))))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2))))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1)))
   A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1)))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1)))
   A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1)))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1)))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1)))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1)))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1)))
   A__U42(tt, tt, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), tt), MARK(tt))
   A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0), MARK(0))
   A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
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   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2)))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2)))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2)))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2)))
   A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2)))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2)))
   A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1))))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0))))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0))))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0))))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1))))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2))))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2))))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1)))
   A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1)))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1)))
   A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1)))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1)))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1)))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1)))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1)))
   A__U42(tt, tt, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), tt), MARK(tt))
   A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0), MARK(0))
   A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(251) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U42(tt, tt, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), tt), MARK(tt))

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

(252)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
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   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2)))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2)))
   A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2)))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2)))
   A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2)))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2)))
   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2)))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2)))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2)))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2)))
   A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2)))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2)))
   A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1))))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0))))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0))))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0))))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1))))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2))))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2))))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1)))
   A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1)))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1)))
   A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1)))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1)))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1)))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1)))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1)))
   A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0), MARK(0))
   A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
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   A__U42(tt, U31(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), tt) -> c11(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, x1), 0) -> c11(A__PLUS(0, a__U31(mark(x0), x1)), MARK(U31(x0, x1)))
   A__U42(tt, U31(x0, z1), x2) -> c11(MARK(U31(x0, z1)))
   A__U42(tt, U31(0, x1), x2) -> c11(A__PLUS(mark(x2), a__U31(0, x1)))
   A__U42(tt, U41(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U11(mark(z0), z1), x1, x2)), MARK(U41(U11(z0, z1), x1, x2)))
   A__U42(tt, U41(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U12(mark(z0)), x1, x2)), MARK(U41(U12(z0), x1, x2)))
   A__U42(tt, U41(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__isNat(z0), x1, x2)), MARK(U41(isNat(z0), x1, x2)))
   A__U42(tt, U41(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U21(mark(z0)), x1, x2)), MARK(U41(U21(z0), x1, x2)))
   A__U42(tt, U41(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U31(mark(z0), z1), x1, x2)), MARK(U41(U31(z0, z1), x1, x2)))
   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2)))
   A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2)))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2)))
   A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2)))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2)))
   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2)))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2)))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2)))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2)))
   A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2)))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2)))
   A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1))))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0))))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0))))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0))))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1))))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2))))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2))))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1)))
   A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1)))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1)))
   A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1)))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1)))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1)))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1)))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1)))
   A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0), MARK(0))
   A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(254)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
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   A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1)))
   A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0))
   A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
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   A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1)))
   A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0))
   A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(255) CdtNarrowingProof (BOTH BOUNDS(ID, ID))
Use narrowing to replace A__U42(tt, x0, U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) by 
   A__U42(tt, U11(z0, z1), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   A__U42(tt, U12(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), a__U12(mark(z0))), MARK(U12(z0)))
   A__U42(tt, isNat(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), a__isNat(z0)), MARK(isNat(z0)))
   A__U42(tt, U21(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), a__U21(mark(z0))), MARK(U21(z0)))
   A__U42(tt, U31(z0, z1), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   A__U42(tt, U41(z0, z1, z2), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U42(z0, z1, z2), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   A__U42(tt, plus(z0, z1), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   A__U42(tt, tt, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), tt), MARK(tt))
   A__U42(tt, s(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, 0, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), 0), MARK(0))
   A__U42(tt, x0, U12(x1)) -> c11(A__PLUS(U12(mark(x1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U12(z0))) -> c11(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(isNat(z0))) -> c11(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U21(z0))) -> c11(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c11(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(tt)) -> c11(A__PLUS(a__U12(tt), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(s(z0))) -> c11(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(0)) -> c11(A__PLUS(a__U12(0), mark(x0)), MARK(x0))

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

(256)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
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   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2)))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2)))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2)))
   A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2)))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2)))
   A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1))))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0))))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0))))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0))))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1))))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2))))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2))))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1)))
   A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1)))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1)))
   A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1)))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1)))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1)))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1)))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1)))
   A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0))
   A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0))
   A__U42(tt, tt, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), tt), MARK(tt))
   A__U42(tt, s(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, 0, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), 0), MARK(0))
   A__U42(tt, x0, U12(x1)) -> c11(A__PLUS(U12(mark(x1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U12(z0))) -> c11(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(isNat(z0))) -> c11(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U21(z0))) -> c11(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c11(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(tt)) -> c11(A__PLUS(a__U12(tt), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(s(z0))) -> c11(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(0)) -> c11(A__PLUS(a__U12(0), mark(x0)), MARK(x0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
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   A__U42(tt, U41(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U41(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U41(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2)))
   A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2)))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2)))
   A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2)))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2)))
   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2)))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2)))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2)))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2)))
   A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2)))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2)))
   A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1))))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0))))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0))))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0))))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1))))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2))))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2))))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1)))
   A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1)))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1)))
   A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1)))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1)))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1)))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1)))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1)))
   A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0))
   A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0))
   A__U42(tt, tt, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), tt), MARK(tt))
   A__U42(tt, s(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, 0, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), 0), MARK(0))
   A__U42(tt, x0, U12(x1)) -> c11(A__PLUS(U12(mark(x1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U12(z0))) -> c11(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(isNat(z0))) -> c11(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U21(z0))) -> c11(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c11(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(tt)) -> c11(A__PLUS(a__U12(tt), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(s(z0))) -> c11(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(0)) -> c11(A__PLUS(a__U12(0), mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

(257) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID))
Removed 1 trailing nodes:
   A__U42(tt, tt, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), tt), MARK(tt))

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

(258)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
   A__U42(tt, U11(U21(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(U31(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U41(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(U42(z0, z1, z2), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U42(mark(z0), z1, z2), x1)), MARK(x2))
   A__U42(tt, U11(plus(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2))
   A__U42(tt, U11(tt, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2))
   A__U42(tt, U11(s(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(0, x1), x2) -> c10(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2))
   A__U42(tt, U11(x0, x1), U11(z0, z1)) -> c10(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1)))
   A__U42(tt, U11(x0, x1), U12(z0)) -> c10(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0)))
   A__U42(tt, U11(x0, x1), isNat(z0)) -> c10(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0)))
   A__U42(tt, U11(x0, x1), U21(z0)) -> c10(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0)))
   A__U42(tt, U11(x0, x1), U31(z0, z1)) -> c10(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1)))
   A__U42(tt, U11(x0, x1), U41(z0, z1, z2)) -> c10(A__PLUS(a__U41(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U41(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), U42(z0, z1, z2)) -> c10(A__PLUS(a__U42(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U42(z0, z1, z2)))
   A__U42(tt, U11(x0, x1), plus(z0, z1)) -> c10(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1)))
   A__U42(tt, U11(x0, x1), s(z0)) -> c10(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0)))
   A__U42(tt, U11(x0, z1), x2) -> c10(MARK(x2))
   A__U42(tt, U11(x0, x1), tt) -> c10(A__PLUS(tt, a__U11(mark(x0), x1)))
   A__U42(tt, U11(x0, x1), 0) -> c10(A__PLUS(0, a__U11(mark(x0), x1)))
   A__U42(tt, U12(U11(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U12(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1))
   A__U42(tt, U12(isNat(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1))
   A__U42(tt, U12(U21(z0)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1))
   A__U42(tt, U12(U31(z0, z1)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1))
   A__U42(tt, U12(U41(z0, z1, z2)), x1) -> c10(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1, z2))), MARK(x1))
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   A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1)))
   A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0))
   A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0))
   A__U42(tt, s(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, 0, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), 0), MARK(0))
   A__U42(tt, x0, U12(x1)) -> c11(A__PLUS(U12(mark(x1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U12(z0))) -> c11(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(isNat(z0))) -> c11(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U21(z0))) -> c11(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c11(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(tt)) -> c11(A__PLUS(a__U12(tt), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(s(z0))) -> c11(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(0)) -> c11(A__PLUS(a__U12(0), mark(x0)), MARK(x0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
   MARK(plus(x0, s(z0))) -> c27(A__PLUS(mark(x0), s(mark(z0))), MARK(x0))
   MARK(plus(x0, 0)) -> c27(A__PLUS(mark(x0), 0), MARK(x0))
   MARK(plus(U11(z0, z1), x1)) -> c27(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1)))
   MARK(plus(U12(z0), x1)) -> c27(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0)))
   MARK(plus(isNat(z0), x1)) -> c27(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0)))
   MARK(plus(U21(z0), x1)) -> c27(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0)))
   MARK(plus(U31(z0, z1), x1)) -> c27(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1)))
   MARK(plus(U41(z0, z1, z2), x1)) -> c27(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(U41(z0, z1, z2)))
   MARK(plus(U42(z0, z1, z2), x1)) -> c27(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(U42(z0, z1, z2)))
   MARK(plus(plus(z0, z1), x1)) -> c27(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1)))
   MARK(plus(s(z0), x1)) -> c27(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0)))
   MARK(plus(x0, tt)) -> c27(MARK(x0))
   MARK(plus(tt, x1)) -> c27(A__PLUS(tt, mark(x1)))
   MARK(plus(0, x1)) -> c27(A__PLUS(0, mark(x1)))
   MARK(plus(x0, U11(z0, z1))) -> c28(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1)))
   MARK(plus(x0, U12(z0))) -> c28(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0)))
   MARK(plus(x0, isNat(z0))) -> c28(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0)))
   MARK(plus(x0, U21(z0))) -> c28(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0)))
   MARK(plus(x0, U31(z0, z1))) -> c28(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1)))
   MARK(plus(x0, U41(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(U41(z0, z1, z2)))
   MARK(plus(x0, U42(z0, z1, z2))) -> c28(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(U42(z0, z1, z2)))
   MARK(plus(x0, plus(z0, z1))) -> c28(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1)))
   MARK(plus(x0, s(z0))) -> c28(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0)))
   MARK(plus(U11(z0, z1), x1)) -> c28(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U12(z0), x1)) -> c28(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(isNat(z0), x1)) -> c28(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1))
   MARK(plus(U21(z0), x1)) -> c28(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(U31(z0, z1), x1)) -> c28(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1))
   MARK(plus(U41(z0, z1, z2), x1)) -> c28(A__PLUS(a__U41(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(U42(z0, z1, z2), x1)) -> c28(A__PLUS(a__U42(mark(z0), z1, z2), mark(x1)), MARK(x1))
   MARK(plus(plus(z0, z1), x1)) -> c28(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1))
   MARK(plus(tt, x1)) -> c28(A__PLUS(tt, mark(x1)), MARK(x1))
   MARK(plus(s(z0), x1)) -> c28(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1))
   MARK(plus(0, x1)) -> c28(A__PLUS(0, mark(x1)), MARK(x1))
   MARK(plus(x0, 0)) -> c28(A__PLUS(mark(x0), 0))
   A__U41(tt, x0, plus(0, x2)) -> c8(A__U42(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2)))
   A__U41(tt, x0, plus(plus(z0, z1), x2)) -> c8(A__U42(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2)))
   A__U41(tt, x0, plus(s(z0), x2)) -> c8(A__U42(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2)))
   A__U41(tt, x0, plus(z0, x2)) -> c8(A__U42(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2)))
   A__U41(tt, x0, plus(x1, z1)) -> c8(A__ISNAT(plus(x1, z1)))
   A__U41(tt, x0, s(0)) -> c8(A__U42(a__U21(tt), x0, s(0)), A__ISNAT(s(0)))
   A__U41(tt, x0, s(plus(z0, z1))) -> c8(A__U42(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1))))
   A__U41(tt, x0, s(s(z0))) -> c8(A__U42(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0))))
   A__U41(tt, x0, s(z0)) -> c8(A__U42(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0)))
   A__U41(tt, x0, s(x1)) -> c8(A__ISNAT(s(x1)))
   A__U42(tt, U11(U11(z0, z1), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2))
   A__U42(tt, U11(U12(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2))
   A__U42(tt, U11(isNat(z0), x1), x2) -> c10(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2))
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   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1)))
   A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1)))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1)))
   A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1)))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1)))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1)))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1)))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1)))
   A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0))
   A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0))
   A__U42(tt, s(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, 0, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), 0), MARK(0))
   A__U42(tt, x0, U12(x1)) -> c11(A__PLUS(U12(mark(x1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U12(z0))) -> c11(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(isNat(z0))) -> c11(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U21(z0))) -> c11(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c11(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(tt)) -> c11(A__PLUS(a__U12(tt), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(s(z0))) -> c11(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(0)) -> c11(A__PLUS(a__U12(0), mark(x0)), MARK(x0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2


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

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

(260)
Obligation:
Complexity Dependency Tuples Problem

Rules:
   a__U11(tt, z0) -> a__U12(a__isNat(z0))
   a__U11(z0, z1) -> U11(z0, z1)
   a__U12(tt) -> tt
   a__U12(z0) -> U12(z0)
   a__U21(tt) -> tt
   a__U21(z0) -> U21(z0)
   a__U31(tt, z0) -> mark(z0)
   a__U31(z0, z1) -> U31(z0, z1)
   a__U41(tt, z0, z1) -> a__U42(a__isNat(z1), z0, z1)
   a__U41(z0, z1, z2) -> U41(z0, z1, z2)
   a__U42(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0)))
   a__U42(z0, z1, z2) -> U42(z0, z1, z2)
   a__isNat(0) -> tt
   a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1)
   a__isNat(s(z0)) -> a__U21(a__isNat(z0))
   a__isNat(z0) -> isNat(z0)
   a__plus(z0, 0) -> a__U31(a__isNat(z0), z0)
   a__plus(z0, s(z1)) -> a__U41(a__isNat(z1), z1, z0)
   a__plus(z0, z1) -> plus(z0, z1)
   mark(U11(z0, z1)) -> a__U11(mark(z0), z1)
   mark(U12(z0)) -> a__U12(mark(z0))
   mark(isNat(z0)) -> a__isNat(z0)
   mark(U21(z0)) -> a__U21(mark(z0))
   mark(U31(z0, z1)) -> a__U31(mark(z0), z1)
   mark(U41(z0, z1, z2)) -> a__U41(mark(z0), z1, z2)
   mark(U42(z0, z1, z2)) -> a__U42(mark(z0), z1, z2)
   mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1))
   mark(tt) -> tt
   mark(s(z0)) -> s(mark(z0))
   mark(0) -> 0
Tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U41(U12(z0), x1, x2)) -> c25(A__U41(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U41(isNat(z0), x1, x2)) -> c25(A__U41(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U41(U21(z0), x1, x2)) -> c25(A__U41(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U41(U31(z0, z1), x1, x2)) -> c25(A__U41(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U41(U41(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U41(U42(z0, z1, z2), x1, x2)) -> c25(A__U41(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U41(plus(z0, z1), x1, x2)) -> c25(A__U41(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U41(tt, x1, x2)) -> c25(A__U41(tt, x1, x2))
   MARK(U41(s(z0), x1, x2)) -> c25(MARK(s(z0)))
   MARK(U42(U11(z0, z1), x1, x2)) -> c26(A__U42(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
   MARK(U42(U12(z0), x1, x2)) -> c26(A__U42(a__U12(mark(z0)), x1, x2), MARK(U12(z0)))
   MARK(U42(isNat(z0), x1, x2)) -> c26(A__U42(a__isNat(z0), x1, x2), MARK(isNat(z0)))
   MARK(U42(U21(z0), x1, x2)) -> c26(A__U42(a__U21(mark(z0)), x1, x2), MARK(U21(z0)))
   MARK(U42(U31(z0, z1), x1, x2)) -> c26(A__U42(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1)))
   MARK(U42(U41(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U41(mark(z0), z1, z2), x1, x2), MARK(U41(z0, z1, z2)))
   MARK(U42(U42(z0, z1, z2), x1, x2)) -> c26(A__U42(a__U42(mark(z0), z1, z2), x1, x2), MARK(U42(z0, z1, z2)))
   MARK(U42(plus(z0, z1), x1, x2)) -> c26(A__U42(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1)))
   MARK(U42(tt, x1, x2)) -> c26(A__U42(tt, x1, x2))
   MARK(U42(s(z0), x1, x2)) -> c26(MARK(s(z0)))
   MARK(plus(x0, U11(z0, z1))) -> c27(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U12(z0))) -> c27(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0))
   MARK(plus(x0, isNat(z0))) -> c27(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0))
   MARK(plus(x0, U21(z0))) -> c27(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0))
   MARK(plus(x0, U31(z0, z1))) -> c27(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0))
   MARK(plus(x0, U41(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U41(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, U42(z0, z1, z2))) -> c27(A__PLUS(mark(x0), a__U42(mark(z0), z1, z2)), MARK(x0))
   MARK(plus(x0, plus(z0, z1))) -> c27(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0))
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   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2)))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2)))
   A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2)))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2)))
   A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1))))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0))))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0))))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0))))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1))))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2))))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2))))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1)))
   A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1)))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1)))
   A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1)))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1)))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1)))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1)))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1)))
   A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0))
   A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0))
   A__U42(tt, s(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U12(x1)) -> c11(A__PLUS(U12(mark(x1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U12(z0))) -> c11(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(isNat(z0))) -> c11(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U21(z0))) -> c11(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c11(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(tt)) -> c11(A__PLUS(a__U12(tt), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(s(z0))) -> c11(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(0)) -> c11(A__PLUS(a__U12(0), mark(x0)), MARK(x0))
   A__U42(tt, 0, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), 0))
S tuples:
   A__U31(tt, z0) -> c6(MARK(z0))
   MARK(isNat(z0)) -> c22(A__ISNAT(z0))
   MARK(s(z0)) -> c30(MARK(z0))
   A__U11(tt, z0) -> c(A__ISNAT(z0))
   A__ISNAT(s(z0)) -> c15(A__ISNAT(z0))
   MARK(U12(z0)) -> c21(MARK(z0))
   MARK(U21(z0)) -> c23(MARK(z0))
   A__U41(tt, x0, 0) -> c8(A__U42(tt, x0, 0))
   A__U41(tt, x0, z0) -> c8(A__ISNAT(z0))
   A__U42(tt, s(z0), x1) -> c10(A__PLUS(mark(x1), s(mark(z0))), MARK(x1))
   A__U42(tt, 0, x1) -> c10(A__PLUS(mark(x1), 0), MARK(x1))
   A__U42(tt, tt, x1) -> c10(MARK(x1))
   A__U42(tt, s(z0), x1) -> c11(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, isNat(z0)) -> c11(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0))
   A__U42(tt, x0, U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), mark(x0)), MARK(x0))
   A__U42(tt, x0, plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, tt) -> c11(A__PLUS(tt, mark(x0)), MARK(x0))
   A__U42(tt, x0, s(z0)) -> c11(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, 0) -> c11(A__PLUS(0, mark(x0)), MARK(x0))
   A__U42(tt, 0, x1) -> c11(A__PLUS(mark(x1), 0))
   A__ISNAT(plus(plus(z0, z1), x1)) -> c14(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1)))
   A__ISNAT(plus(s(z0), x1)) -> c14(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0)))
   A__ISNAT(plus(0, x1)) -> c14(A__U11(tt, x1))
   A__ISNAT(plus(z0, x1)) -> c14(A__ISNAT(z0))
   A__PLUS(plus(z0, z1), 0) -> c17(A__U31(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1)))
   A__PLUS(s(z0), 0) -> c17(A__U31(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0)))
   A__PLUS(0, 0) -> c17(A__U31(tt, 0))
   A__PLUS(z0, 0) -> c17(A__ISNAT(z0))
   A__PLUS(x0, s(plus(z0, z1))) -> c18(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1)))
   A__PLUS(x0, s(s(z0))) -> c18(A__U41(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0)))
   A__PLUS(x0, s(0)) -> c18(A__U41(tt, 0, x0))
   A__PLUS(x0, s(z0)) -> c18(A__ISNAT(z0))
   MARK(U11(U11(z0, z1), x1)) -> c20(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U11(U12(z0), x1)) -> c20(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U11(U21(z0), x1)) -> c20(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U11(U31(z0, z1), x1)) -> c20(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U11(U41(z0, z1, z2), x1)) -> c20(A__U11(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U11(U42(z0, z1, z2), x1)) -> c20(A__U11(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U11(plus(z0, z1), x1)) -> c20(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U11(tt, x1)) -> c20(A__U11(tt, x1))
   MARK(U11(s(z0), x1)) -> c20(MARK(s(z0)))
   MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1))
   MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0)))
   MARK(U31(U11(z0, z1), x1)) -> c24(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1)))
   MARK(U31(U12(z0), x1)) -> c24(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0)))
   MARK(U31(isNat(z0), x1)) -> c24(A__U31(a__isNat(z0), x1), MARK(isNat(z0)))
   MARK(U31(U21(z0), x1)) -> c24(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0)))
   MARK(U31(U31(z0, z1), x1)) -> c24(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1)))
   MARK(U31(U41(z0, z1, z2), x1)) -> c24(A__U31(a__U41(mark(z0), z1, z2), x1), MARK(U41(z0, z1, z2)))
   MARK(U31(U42(z0, z1, z2), x1)) -> c24(A__U31(a__U42(mark(z0), z1, z2), x1), MARK(U42(z0, z1, z2)))
   MARK(U31(plus(z0, z1), x1)) -> c24(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1)))
   MARK(U31(tt, x1)) -> c24(A__U31(tt, x1))
   MARK(U31(s(z0), x1)) -> c24(MARK(s(z0)))
   MARK(U41(U11(z0, z1), x1, x2)) -> c25(A__U41(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1)))
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   A__U42(tt, U41(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U41(plus(z0, z1), x1, x2)))
   A__U42(tt, U41(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(tt, x1, x2)), MARK(U41(tt, x1, x2)))
   A__U42(tt, U41(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(s(mark(z0)), x1, x2)), MARK(U41(s(z0), x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U41(mark(x0), x1, x2)), MARK(U41(x0, x1, x2)))
   A__U42(tt, U41(x0, z1, z2), x3) -> c11(MARK(U41(x0, z1, z2)))
   A__U42(tt, U41(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U41(0, x1, x2)))
   A__U42(tt, U42(U11(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U11(mark(z0), z1), x1, x2)), MARK(U42(U11(z0, z1), x1, x2)))
   A__U42(tt, U42(U12(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U12(mark(z0)), x1, x2)), MARK(U42(U12(z0), x1, x2)))
   A__U42(tt, U42(isNat(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__isNat(z0), x1, x2)), MARK(U42(isNat(z0), x1, x2)))
   A__U42(tt, U42(U21(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U21(mark(z0)), x1, x2)), MARK(U42(U21(z0), x1, x2)))
   A__U42(tt, U42(U31(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U31(mark(z0), z1), x1, x2)), MARK(U42(U31(z0, z1), x1, x2)))
   A__U42(tt, U42(U41(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U41(mark(z0), z1, z2), x1, x2)), MARK(U42(U41(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(U42(z0, z1, z2), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__U42(mark(z0), z1, z2), x1, x2)), MARK(U42(U42(z0, z1, z2), x1, x2)))
   A__U42(tt, U42(plus(z0, z1), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(U42(plus(z0, z1), x1, x2)))
   A__U42(tt, U42(tt, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(tt, x1, x2)), MARK(U42(tt, x1, x2)))
   A__U42(tt, U42(s(z0), x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(s(mark(z0)), x1, x2)), MARK(U42(s(z0), x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), tt) -> c11(A__PLUS(tt, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, x1, x2), 0) -> c11(A__PLUS(0, a__U42(mark(x0), x1, x2)), MARK(U42(x0, x1, x2)))
   A__U42(tt, U42(x0, z1, z2), x3) -> c11(MARK(U42(x0, z1, z2)))
   A__U42(tt, U42(0, x1, x2), x3) -> c11(A__PLUS(mark(x3), a__U42(0, x1, x2)))
   A__U42(tt, plus(x0, U11(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U11(mark(z0), z1))), MARK(plus(x0, U11(z0, z1))))
   A__U42(tt, plus(x0, U12(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U12(mark(z0)))), MARK(plus(x0, U12(z0))))
   A__U42(tt, plus(x0, isNat(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__isNat(z0))), MARK(plus(x0, isNat(z0))))
   A__U42(tt, plus(x0, U21(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U21(mark(z0)))), MARK(plus(x0, U21(z0))))
   A__U42(tt, plus(x0, U31(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U31(mark(z0), z1))), MARK(plus(x0, U31(z0, z1))))
   A__U42(tt, plus(x0, U41(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U41(mark(z0), z1, z2))), MARK(plus(x0, U41(z0, z1, z2))))
   A__U42(tt, plus(x0, U42(z0, z1, z2)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__U42(mark(z0), z1, z2))), MARK(plus(x0, U42(z0, z1, z2))))
   A__U42(tt, plus(x0, plus(z0, z1)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), a__plus(mark(z0), mark(z1)))), MARK(plus(x0, plus(z0, z1))))
   A__U42(tt, plus(x0, tt), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), tt)), MARK(plus(x0, tt)))
   A__U42(tt, plus(x0, s(z0)), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), s(mark(z0)))), MARK(plus(x0, s(z0))))
   A__U42(tt, plus(x0, 0), x2) -> c11(A__PLUS(mark(x2), a__plus(mark(x0), 0)), MARK(plus(x0, 0)))
   A__U42(tt, plus(U11(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U11(mark(z0), z1), mark(x1))), MARK(plus(U11(z0, z1), x1)))
   A__U42(tt, plus(U12(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U12(mark(z0)), mark(x1))), MARK(plus(U12(z0), x1)))
   A__U42(tt, plus(isNat(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__isNat(z0), mark(x1))), MARK(plus(isNat(z0), x1)))
   A__U42(tt, plus(U21(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U21(mark(z0)), mark(x1))), MARK(plus(U21(z0), x1)))
   A__U42(tt, plus(U31(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U31(mark(z0), z1), mark(x1))), MARK(plus(U31(z0, z1), x1)))
   A__U42(tt, plus(U41(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U41(mark(z0), z1, z2), mark(x1))), MARK(plus(U41(z0, z1, z2), x1)))
   A__U42(tt, plus(U42(z0, z1, z2), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__U42(mark(z0), z1, z2), mark(x1))), MARK(plus(U42(z0, z1, z2), x1)))
   A__U42(tt, plus(plus(z0, z1), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(a__plus(mark(z0), mark(z1)), mark(x1))), MARK(plus(plus(z0, z1), x1)))
   A__U42(tt, plus(tt, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(tt, mark(x1))), MARK(plus(tt, x1)))
   A__U42(tt, plus(s(z0), x1), x2) -> c11(A__PLUS(mark(x2), a__plus(s(mark(z0)), mark(x1))), MARK(plus(s(z0), x1)))
   A__U42(tt, plus(0, x1), x2) -> c11(A__PLUS(mark(x2), a__plus(0, mark(x1))), MARK(plus(0, x1)))
   A__U42(tt, plus(x0, x1), U11(z0, z1)) -> c11(A__PLUS(a__U11(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U12(z0)) -> c11(A__PLUS(a__U12(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), isNat(z0)) -> c11(A__PLUS(a__isNat(z0), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U21(z0)) -> c11(A__PLUS(a__U21(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U31(z0, z1)) -> c11(A__PLUS(a__U31(mark(z0), z1), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U41(z0, z1, z2)) -> c11(A__PLUS(a__U41(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), U42(z0, z1, z2)) -> c11(A__PLUS(a__U42(mark(z0), z1, z2), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), plus(z0, z1)) -> c11(A__PLUS(a__plus(mark(z0), mark(z1)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), tt) -> c11(A__PLUS(tt, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), s(z0)) -> c11(A__PLUS(s(mark(z0)), a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), 0) -> c11(A__PLUS(0, a__plus(mark(x0), mark(x1))), MARK(plus(x0, x1)))
   A__U42(tt, plus(x0, x1), x2) -> c11(MARK(plus(x0, x1)))
   A__U42(tt, s(z0), U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U11(x1, z1)) -> c11(A__PLUS(U11(mark(x1), z1), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U11(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U11(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U12(z0), x2)) -> c11(A__PLUS(a__U11(a__U12(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(isNat(z0), x2)) -> c11(A__PLUS(a__U11(a__isNat(z0), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U21(z0), x2)) -> c11(A__PLUS(a__U11(a__U21(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U31(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__U31(mark(z0), z1), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U41(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U41(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(U42(z0, z1, z2), x2)) -> c11(A__PLUS(a__U11(a__U42(mark(z0), z1, z2), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(plus(z0, z1), x2)) -> c11(A__PLUS(a__U11(a__plus(mark(z0), mark(z1)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(tt, x2)) -> c11(A__PLUS(a__U11(tt, x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(s(z0), x2)) -> c11(A__PLUS(a__U11(s(mark(z0)), x2), mark(x0)), MARK(x0))
   A__U42(tt, x0, U11(0, x2)) -> c11(A__PLUS(a__U11(0, x2), mark(x0)), MARK(x0))
   A__U42(tt, 0, U11(x1, x2)) -> c11(A__PLUS(a__U11(mark(x1), x2), 0))
   A__U42(tt, s(z0), U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), s(mark(z0))), MARK(s(z0)))
   A__U42(tt, x0, U12(x1)) -> c11(A__PLUS(U12(mark(x1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U11(z0, z1))) -> c11(A__PLUS(a__U12(a__U11(mark(z0), z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U12(z0))) -> c11(A__PLUS(a__U12(a__U12(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(isNat(z0))) -> c11(A__PLUS(a__U12(a__isNat(z0)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U21(z0))) -> c11(A__PLUS(a__U12(a__U21(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U31(z0, z1))) -> c11(A__PLUS(a__U12(a__U31(mark(z0), z1)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U41(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U41(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(U42(z0, z1, z2))) -> c11(A__PLUS(a__U12(a__U42(mark(z0), z1, z2)), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(plus(z0, z1))) -> c11(A__PLUS(a__U12(a__plus(mark(z0), mark(z1))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(tt)) -> c11(A__PLUS(a__U12(tt), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(s(z0))) -> c11(A__PLUS(a__U12(s(mark(z0))), mark(x0)), MARK(x0))
   A__U42(tt, x0, U12(0)) -> c11(A__PLUS(a__U12(0), mark(x0)), MARK(x0))
   A__U42(tt, 0, U12(x1)) -> c11(A__PLUS(a__U12(mark(x1)), 0))
K tuples:none
Defined Rule Symbols:   a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U41_3, a__U42_3, a__isNat_1, a__plus_2, mark_1

Defined Pair Symbols:   A__U31_2, MARK_1, A__U11_2, A__ISNAT_1, A__U41_3, A__U42_3, A__PLUS_2

Compound Symbols:   c6_1, c22_1, c30_1, c_1, c15_1, c21_1, c23_1, c8_1, c10_2, c10_1, c11_2, c11_1, c14_2, c14_1, c17_2, c17_1, c18_2, c18_1, c20_2, c20_1, c1_1, c24_2, c24_1, c25_2, c25_1, c26_2, c26_1, c27_2, c27_1, c28_2, c28_1, c8_2